LMFDB - Embedded newform 471.2.e.c.301.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(169,471)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("471.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			301.4
Character	$\chi$	$=$	471.301
Dual form			471.2.e.c.169.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.21741 q^{2} +(-0.500000 + 0.866025i) q^{3} -0.517920 q^{4} +(-1.98968 + 3.44622i) q^{5} +(0.608704 - 1.05431i) q^{6} +2.72799 q^{7} +3.06533 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-1.21741 q^{2} +(-0.500000 + 0.866025i) q^{3} -0.517920 q^{4} +(-1.98968 + 3.44622i) q^{5} +(0.608704 - 1.05431i) q^{6} +2.72799 q^{7} +3.06533 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.42225 - 4.19545i) q^{10} +(-1.10379 + 1.91181i) q^{11} +(0.258960 - 0.448531i) q^{12} +(3.38898 + 5.86988i) q^{13} -3.32108 q^{14} +(-1.98968 - 3.44622i) q^{15} -2.69592 q^{16} +(-0.929972 + 1.61076i) q^{17} +(0.608704 + 1.05431i) q^{18} +(0.0693030 - 0.120036i) q^{19} +(1.03049 - 1.78486i) q^{20} +(-1.36400 + 2.36251i) q^{21} +(1.34376 - 2.32745i) q^{22} -0.480350 q^{23} +(-1.53267 + 2.65466i) q^{24} +(-5.41761 - 9.38358i) q^{25} +(-4.12577 - 7.14604i) q^{26} +1.00000 q^{27} -1.41288 q^{28} -9.21492 q^{29} +(2.42225 + 4.19545i) q^{30} +(-5.29735 - 9.17528i) q^{31} -2.84863 q^{32} +(-1.10379 - 1.91181i) q^{33} +(1.13215 - 1.96095i) q^{34} +(-5.42782 + 9.40126i) q^{35} +(0.258960 + 0.448531i) q^{36} +(2.12822 + 3.68619i) q^{37} +(-0.0843700 + 0.146133i) q^{38} -6.77796 q^{39} +(-6.09902 + 10.5638i) q^{40} +11.8306 q^{41} +(1.66054 - 2.87614i) q^{42} +(-1.05606 - 1.82914i) q^{43} +(0.571672 - 0.990165i) q^{44} +3.97935 q^{45} +0.584781 q^{46} +(-0.333636 - 0.577875i) q^{47} +(1.34796 - 2.33474i) q^{48} +0.441952 q^{49} +(6.59544 + 11.4236i) q^{50} +(-0.929972 - 1.61076i) q^{51} +(-1.75522 - 3.04013i) q^{52} +(4.15614 + 7.19864i) q^{53} -1.21741 q^{54} +(-4.39235 - 7.60777i) q^{55} +8.36221 q^{56} +(0.0693030 + 0.120036i) q^{57} +11.2183 q^{58} -4.30756 q^{59} +(1.03049 + 1.78486i) q^{60} +(-3.04830 + 5.27981i) q^{61} +(6.44904 + 11.1701i) q^{62} +(-1.36400 - 2.36251i) q^{63} +8.85979 q^{64} -26.9719 q^{65} +(1.34376 + 2.32745i) q^{66} -1.96419 q^{67} +(0.481651 - 0.834243i) q^{68} +(0.240175 - 0.415995i) q^{69} +(6.60787 - 11.4452i) q^{70} +(3.09041 + 5.35276i) q^{71} +(-1.53267 - 2.65466i) q^{72} +(0.613864 - 1.06324i) q^{73} +(-2.59091 - 4.48759i) q^{74} +10.8352 q^{75} +(-0.0358934 + 0.0621692i) q^{76} +(-3.01112 + 5.21541i) q^{77} +8.25153 q^{78} +4.72471 q^{79} +(5.36401 - 9.29073i) q^{80} +(-0.500000 + 0.866025i) q^{81} -14.4026 q^{82} +(-4.51645 - 7.82271i) q^{83} +(0.706441 - 1.22359i) q^{84} +(-3.70068 - 6.40977i) q^{85} +(1.28565 + 2.22681i) q^{86} +(4.60746 - 7.98036i) q^{87} +(-3.38347 + 5.86034i) q^{88} +(6.69258 - 11.5919i) q^{89} -4.84449 q^{90} +(9.24511 + 16.0130i) q^{91} +0.248783 q^{92} +10.5947 q^{93} +(0.406171 + 0.703510i) q^{94} +(0.275781 + 0.477667i) q^{95} +(1.42432 - 2.46699i) q^{96} +(-3.92032 - 6.79019i) q^{97} -0.538036 q^{98} +2.20757 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9}+O(q^{10}) $ 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9} - q^{10} + 2 q^{11} - 13 q^{12} - 14 q^{14} - 2 q^{15} + 14 q^{16} + 3 q^{17} - q^{18} - 11 q^{19} + q^{20} - 2 q^{21} - 2 q^{22} - 6 q^{23} - 20 q^{25} + 12 q^{26} + 28 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 14 q^{31} + 12 q^{32} + 2 q^{33} - 15 q^{34} - 13 q^{35} - 13 q^{36} - q^{37} + 18 q^{38} - 8 q^{40} + 16 q^{41} + 7 q^{42} - 16 q^{43} + 12 q^{44} + 4 q^{45} + 16 q^{46} - 29 q^{47} - 7 q^{48} + 44 q^{49} - 29 q^{50} + 3 q^{51} + 27 q^{52} + 6 q^{53} + 2 q^{54} - 29 q^{55} - 26 q^{56} - 11 q^{57} + 62 q^{58} - 8 q^{59} + q^{60} + 14 q^{61} + 52 q^{62} - 2 q^{63} + 16 q^{64} - 52 q^{65} - 2 q^{66} + 36 q^{67} + 6 q^{68} + 3 q^{69} - 37 q^{70} - 27 q^{71} - 10 q^{73} - 5 q^{74} + 40 q^{75} - 43 q^{76} + 11 q^{77} - 24 q^{78} - 16 q^{79} - 26 q^{80} - 14 q^{81} - 24 q^{82} + 12 q^{83} - q^{84} + 12 q^{85} - 56 q^{86} + 5 q^{87} + 47 q^{88} - 13 q^{89} + 2 q^{90} + 13 q^{91} - 50 q^{92} + 28 q^{93} - 40 q^{94} - 7 q^{95} - 6 q^{96} + 6 q^{97} - 46 q^{98} - 4 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9 - q^10 + 2 * q^11 - 13 * q^12 - 14 * q^14 - 2 * q^15 + 14 * q^16 + 3 * q^17 - q^18 - 11 * q^19 + q^20 - 2 * q^21 - 2 * q^22 - 6 * q^23 - 20 * q^25 + 12 * q^26 + 28 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 14 * q^31 + 12 * q^32 + 2 * q^33 - 15 * q^34 - 13 * q^35 - 13 * q^36 - q^37 + 18 * q^38 - 8 * q^40 + 16 * q^41 + 7 * q^42 - 16 * q^43 + 12 * q^44 + 4 * q^45 + 16 * q^46 - 29 * q^47 - 7 * q^48 + 44 * q^49 - 29 * q^50 + 3 * q^51 + 27 * q^52 + 6 * q^53 + 2 * q^54 - 29 * q^55 - 26 * q^56 - 11 * q^57 + 62 * q^58 - 8 * q^59 + q^60 + 14 * q^61 + 52 * q^62 - 2 * q^63 + 16 * q^64 - 52 * q^65 - 2 * q^66 + 36 * q^67 + 6 * q^68 + 3 * q^69 - 37 * q^70 - 27 * q^71 - 10 * q^73 - 5 * q^74 + 40 * q^75 - 43 * q^76 + 11 * q^77 - 24 * q^78 - 16 * q^79 - 26 * q^80 - 14 * q^81 - 24 * q^82 + 12 * q^83 - q^84 + 12 * q^85 - 56 * q^86 + 5 * q^87 + 47 * q^88 - 13 * q^89 + 2 * q^90 + 13 * q^91 - 50 * q^92 + 28 * q^93 - 40 * q^94 - 7 * q^95 - 6 * q^96 + 6 * q^97 - 46 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.21741			−0.860837			−0.430418	−	0.902629i	$-0.641634\pi$
$2$	−1.21741			−0.860837			−0.430418	+	0.902629i	$0.641634\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.517920			−0.258960
$5$	−1.98968	+	3.44622i	−0.889810	+	1.54120i	−0.0497101	+	0.998764i	$0.515830\pi$
$5$	−1.98968	+	3.44622i	−0.889810	+	1.54120i	−0.840100	+	0.542432i	$0.817504\pi$
$6$	0.608704	−	1.05431i	0.248502	−	0.430418i
$7$	2.72799			1.03108			0.515542	−	0.856864i	$-0.327590\pi$
$7$	2.72799			1.03108			0.515542	+	0.856864i	$0.327590\pi$
$8$	3.06533			1.08376
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	2.42225	−	4.19545i	0.765981	−	1.32672i
$11$	−1.10379	+	1.91181i	−0.332804	+	0.576433i	−0.983060	−	0.183281i	$-0.941328\pi$
$11$	−1.10379	+	1.91181i	−0.332804	+	0.576433i	0.650257	+	0.759715i	$0.274661\pi$
$12$	0.258960	−	0.448531i	0.0747552	−	0.129480i
$13$	3.38898	+	5.86988i	0.939933	+	1.62801i	0.765591	+	0.643327i	$0.222446\pi$
$13$	3.38898	+	5.86988i	0.939933	+	1.62801i	0.174342	+	0.984685i	$0.444220\pi$
$14$	−3.32108			−0.887596
$15$	−1.98968	−	3.44622i	−0.513732	−	0.889810i
$16$	−2.69592			−0.673980
$17$	−0.929972	+	1.61076i	−0.225551	+	0.390666i	−0.956485	−	0.291782i	$-0.905752\pi$
$17$	−0.929972	+	1.61076i	−0.225551	+	0.390666i	0.730933	+	0.682449i	$0.239085\pi$
$18$	0.608704	+	1.05431i	0.143473	+	0.248502i
$19$	0.0693030	−	0.120036i	0.0158992	−	0.0275382i	−0.857966	−	0.513706i	$-0.828272\pi$
$19$	0.0693030	−	0.120036i	0.0158992	−	0.0275382i	0.873866	+	0.486168i	$0.161606\pi$
$20$	1.03049	−	1.78486i	0.230425	−	0.399108i
$21$	−1.36400	+	2.36251i	−0.297649	+	0.515542i
$22$	1.34376	−	2.32745i	0.286490	−	0.496215i
$23$	−0.480350			−0.100160			−0.0500799	−	0.998745i	$-0.515948\pi$
$23$	−0.480350			−0.100160			−0.0500799	+	0.998745i	$0.515948\pi$
$24$	−1.53267	+	2.65466i	−0.312854	+	0.541880i
$25$	−5.41761	−	9.38358i	−1.08352	−	1.87672i
$26$	−4.12577	−	7.14604i	−0.809129	−	1.40145i
$27$	1.00000			0.192450
$28$	−1.41288			−0.267009
$29$	−9.21492			−1.71117			−0.855584	−	0.517664i	$-0.826802\pi$
$29$	−9.21492			−1.71117			−0.855584	+	0.517664i	$0.826802\pi$
$30$	2.42225	+	4.19545i	0.442239	+	0.765981i
$31$	−5.29735	−	9.17528i	−0.951433	−	1.64793i	−0.742328	−	0.670036i	$-0.766279\pi$
$31$	−5.29735	−	9.17528i	−0.951433	−	1.64793i	−0.209104	−	0.977893i	$-0.567055\pi$
$32$	−2.84863			−0.503572
$33$	−1.10379	−	1.91181i	−0.192144	−	0.332804i
$34$	1.13215	−	1.96095i	0.194163	−	0.336300i
$35$	−5.42782	+	9.40126i	−0.917469	+	1.58910i
$36$	0.258960	+	0.448531i	0.0431600	+	0.0747552i
$37$	2.12822	+	3.68619i	0.349877	+	0.606005i	0.986227	−	0.165395i	$-0.0528899\pi$
$37$	2.12822	+	3.68619i	0.349877	+	0.606005i	−0.636350	+	0.771400i	$0.719557\pi$
$38$	−0.0843700	+	0.146133i	−0.0136866	+	0.0237059i
$39$	−6.77796			−1.08534
$40$	−6.09902	+	10.5638i	−0.964339	+	1.67028i
$41$	11.8306			1.84763			0.923813	−	0.382844i	$-0.125055\pi$
$41$	11.8306			1.84763			0.923813	+	0.382844i	$0.125055\pi$
$42$	1.66054	−	2.87614i	0.256227	−	0.443798i
$43$	−1.05606	−	1.82914i	−0.161047	−	0.278942i	0.774197	−	0.632944i	$-0.218154\pi$
$43$	−1.05606	−	1.82914i	−0.161047	−	0.278942i	−0.935245	+	0.354002i	$0.884820\pi$
$44$	0.571672	−	0.990165i	0.0861828	−	0.149273i
$45$	3.97935			0.593207
$46$	0.584781			0.0862213
$47$	−0.333636	−	0.577875i	−0.0486659	−	0.0842918i	0.840666	−	0.541553i	$-0.182164\pi$
$47$	−0.333636	−	0.577875i	−0.0486659	−	0.0842918i	−0.889332	+	0.457262i	$0.848830\pi$
$48$	1.34796	−	2.33474i	0.194561	−	0.336990i
$49$	0.441952			0.0631360
$50$	6.59544	+	11.4236i	0.932737	+	1.61555i
$51$	−0.929972	−	1.61076i	−0.130222	−	0.225551i
$52$	−1.75522	−	3.04013i	−0.243405	−	0.421590i
$53$	4.15614	+	7.19864i	0.570889	+	0.988809i	0.996475	+	0.0838910i	$0.0267347\pi$
$53$	4.15614	+	7.19864i	0.570889	+	0.988809i	−0.425586	+	0.904918i	$0.639932\pi$
$54$	−1.21741			−0.165668
$55$	−4.39235	−	7.60777i	−0.592264	−	1.02583i
$56$	8.36221			1.11745
$57$	0.0693030	+	0.120036i	0.00917941	+	0.0158992i
$58$	11.2183			1.47304
$59$	−4.30756			−0.560796			−0.280398	−	0.959884i	$-0.590466\pi$
$59$	−4.30756			−0.560796			−0.280398	+	0.959884i	$0.590466\pi$
$60$	1.03049	+	1.78486i	0.133036	+	0.230425i
$61$	−3.04830	+	5.27981i	−0.390295	+	0.676011i	−0.992488	−	0.122339i	$-0.960960\pi$
$61$	−3.04830	+	5.27981i	−0.390295	+	0.676011i	0.602193	+	0.798350i	$0.294294\pi$
$62$	6.44904	+	11.1701i	0.819028	+	1.41860i
$63$	−1.36400	−	2.36251i	−0.171847	−	0.297649i
$64$	8.85979			1.10747
$65$	−26.9719			−3.34545
$66$	1.34376	+	2.32745i	0.165405	+	0.286490i
$67$	−1.96419			−0.239964			−0.119982	−	0.992776i	$-0.538284\pi$
$67$	−1.96419			−0.239964			−0.119982	+	0.992776i	$0.538284\pi$
$68$	0.481651	−	0.834243i	0.0584087	−	0.101167i
$69$	0.240175	−	0.415995i	0.0289137	−	0.0500799i
$70$	6.60787	−	11.4452i	0.789792	−	1.36796i
$71$	3.09041	+	5.35276i	0.366765	+	0.635255i	0.989058	−	0.147529i	$-0.0471321\pi$
$71$	3.09041	+	5.35276i	0.366765	+	0.635255i	−0.622293	+	0.782784i	$0.713799\pi$
$72$	−1.53267	−	2.65466i	−0.180627	−	0.312854i
$73$	0.613864	−	1.06324i	0.0718473	−	0.124443i	−0.827864	−	0.560929i	$-0.810444\pi$
$73$	0.613864	−	1.06324i	0.0718473	−	0.124443i	0.899711	+	0.436486i	$0.143777\pi$
$74$	−2.59091	−	4.48759i	−0.301187	−	0.521672i
$75$	10.8352			1.25114
$76$	−0.0358934	+	0.0621692i	−0.00411725	+	0.00713129i
$77$	−3.01112	+	5.21541i	−0.343149	+	0.594351i
$78$	8.25153			0.934302
$79$	4.72471			0.531571			0.265786	−	0.964032i	$-0.414369\pi$
$79$	4.72471			0.531571			0.265786	+	0.964032i	$0.414369\pi$
$80$	5.36401	−	9.29073i	0.599714	−	1.03874i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−14.4026			−1.59050
$83$	−4.51645	−	7.82271i	−0.495744	−	0.858654i	0.504244	−	0.863561i	$-0.331771\pi$
$83$	−4.51645	−	7.82271i	−0.495744	−	0.858654i	−0.999988	+	0.00490699i	$0.998438\pi$
$84$	0.706441	−	1.22359i	0.0770790	−	0.133505i
$85$	−3.70068	−	6.40977i	−0.401396	−	0.695237i
$86$	1.28565	+	2.22681i	0.138635	+	0.240123i
$87$	4.60746	−	7.98036i	0.493972	−	0.855584i
$88$	−3.38347	+	5.86034i	−0.360679	+	0.624715i
$89$	6.69258	−	11.5919i	0.709413	−	1.22874i	−0.255663	−	0.966766i	$-0.582294\pi$
$89$	6.69258	−	11.5919i	0.709413	−	1.22874i	0.965075	−	0.261972i	$-0.0843730\pi$
$90$	−4.84449			−0.510654
$91$	9.24511	+	16.0130i	0.969151	+	1.67862i
$92$	0.248783			0.0259374
$93$	10.5947			1.09862
$94$	0.406171	+	0.703510i	0.0418934	+	0.0725615i
$95$	0.275781	+	0.477667i	0.0282945	+	0.0490076i
$96$	1.42432	−	2.46699i	0.145369	−	0.251786i
$97$	−3.92032	−	6.79019i	−0.398048	−	0.689439i	0.595437	−	0.803402i	$-0.296979\pi$
$97$	−3.92032	−	6.79019i	−0.398048	−	0.689439i	−0.993485	+	0.113963i	$0.963645\pi$
$98$	−0.538036			−0.0543498
$99$	2.20757			0.221869
$100$	2.80589	+	4.85994i	0.280589	+	0.485994i
$101$	−9.44746			−0.940057			−0.470028	−	0.882651i	$-0.655756\pi$
$101$	−9.44746			−0.940057			−0.470028	+	0.882651i	$0.655756\pi$
$102$	1.13215	+	1.96095i	0.112100	+	0.194163i
$103$	17.0479			1.67978			0.839889	−	0.542758i	$-0.182620\pi$
$103$	17.0479			1.67978			0.839889	+	0.542758i	$0.182620\pi$
$104$	10.3883	+	17.9931i	1.01866	+	1.76437i
$105$	−5.42782	−	9.40126i	−0.529701	−	0.917469i
$106$	−5.05971	−	8.76367i	−0.491442	−	0.851203i
$107$	−3.35971	−	5.81919i	−0.324795	−	0.562562i	0.656676	−	0.754173i	$-0.271962\pi$
$107$	−3.35971	−	5.81919i	−0.324795	−	0.562562i	−0.981471	+	0.191611i	$0.938629\pi$
$108$	−0.517920			−0.0498368
$109$	−8.03508	+	13.9172i	−0.769621	+	1.33302i	0.168147	+	0.985762i	$0.446222\pi$
$109$	−8.03508	+	13.9172i	−0.769621	+	1.33302i	−0.937768	+	0.347261i	$0.887112\pi$
$110$	5.34728	+	9.26176i	0.509843	+	0.883074i
$111$	−4.25644			−0.404004
$112$	−7.35445			−0.694931
$113$	−1.92899	+	3.34111i	−0.181464	+	0.314305i	−0.942379	−	0.334546i	$-0.891417\pi$
$113$	−1.92899	+	3.34111i	−0.181464	+	0.314305i	0.760915	+	0.648851i	$0.224750\pi$
$114$	−0.0843700	−	0.146133i	−0.00790198	−	0.0136866i
$115$	0.955740	−	1.65539i	0.0891232	−	0.154366i
$116$	4.77259			0.443124
$117$	3.38898	−	5.86988i	0.313311	−	0.542671i
$118$	5.24405			0.482754
$119$	−2.53696	+	4.39414i	−0.232563	+	0.402810i
$120$	−6.09902	−	10.5638i	−0.556762	−	0.964339i
$121$	3.06332	+	5.30582i	0.278483	+	0.482347i
$122$	3.71103	−	6.42768i	0.335980	−	0.581935i
$123$	−5.91529	+	10.2456i	−0.533364	+	0.923813i
$124$	2.74360	+	4.75206i	0.246383	+	0.426747i
$125$	23.2204			2.07690
$126$	1.66054	+	2.87614i	0.147933	+	0.256227i
$127$	1.84153	+	3.18962i	0.163409	+	0.283033i	0.936089	−	0.351763i	$-0.114418\pi$
$127$	1.84153	+	3.18962i	0.163409	+	0.283033i	−0.772680	+	0.634796i	$0.781084\pi$
$128$	−5.08870			−0.449782
$129$	2.11211			0.185961
$130$	32.8357			2.87988
$131$	−3.74110	−	6.47978i	−0.326861	−	0.566141i	0.655026	−	0.755606i	$-0.272658\pi$
$131$	−3.74110	−	6.47978i	−0.326861	−	0.566141i	−0.981887	+	0.189466i	$0.939324\pi$
$132$	0.571672	+	0.990165i	0.0497577	+	0.0861828i
$133$	0.189058	−	0.327458i	0.0163934	−	0.0283943i
$134$	2.39122			0.206570
$135$	−1.98968	+	3.44622i	−0.171244	+	0.296603i
$136$	−2.85067	+	4.93751i	−0.244443	+	0.423388i
$137$	4.68429	−	8.11343i	0.400206	−	0.693177i	−0.593545	−	0.804801i	$-0.702272\pi$
$137$	4.68429	−	8.11343i	0.400206	−	0.693177i	0.993750	+	0.111624i	$0.0356053\pi$
$138$	−0.292391	+	0.506435i	−0.0248899	+	0.0431106i
$139$	6.70675	+	11.6164i	0.568859	+	0.985293i	0.996679	+	0.0814289i	$0.0259484\pi$
$139$	6.70675	+	11.6164i	0.568859	+	0.985293i	−0.427820	+	0.903864i	$0.640718\pi$
$140$	2.81118	−	4.86910i	0.237588	−	0.411514i
$141$	0.667273			0.0561945
$142$	−3.76229	−	6.51648i	−0.315725	−	0.546851i
$143$	−14.9628			−1.25125
$144$	1.34796	+	2.33474i	0.112330	+	0.194561i
$145$	18.3347	−	31.7566i	1.52261	−	2.63724i
$146$	−0.747322	+	1.29440i	−0.0618488	+	0.107125i
$147$	−0.220976	+	0.382742i	−0.0182258	+	0.0315680i
$148$	−1.10225	−	1.90915i	−0.0906042	−	0.156931i
$149$	2.00505			0.164260			0.0821302	−	0.996622i	$-0.473828\pi$
$149$	2.00505			0.164260			0.0821302	+	0.996622i	$0.473828\pi$
$150$	−13.1909			−1.07703
$151$	1.76752	−	3.06143i	0.143838	−	0.249135i	−0.785101	−	0.619368i	$-0.787389\pi$
$151$	1.76752	−	3.06143i	0.143838	−	0.249135i	0.928939	+	0.370233i	$0.120722\pi$
$152$	0.212437	−	0.367951i	0.0172309	−	0.0298448i
$153$	1.85994			0.150368
$154$	3.66576	−	6.34928i	0.295395	−	0.511640i
$155$	42.1600			3.38638
$156$	3.51044			0.281060
$157$	−9.18653	−	8.52102i	−0.733165	−	0.680051i
$157$	−9.18653	−	8.52102i	−0.733165	−	0.680051i
$158$	−5.75189			−0.457596
$159$	−8.31227			−0.659206
$160$	5.66786	−	9.81702i	0.448083	−	0.776103i
$161$	−1.31039			−0.103273
$162$	0.608704	−	1.05431i	0.0478243	−	0.0828341i
$163$	−8.08299	+	14.0002i	−0.633109	+	1.09658i	0.353803	+	0.935320i	$0.384888\pi$
$163$	−8.08299	+	14.0002i	−0.633109	+	1.09658i	−0.986912	+	0.161257i	$0.948445\pi$
$164$	−6.12729			−0.478461
$165$	8.78470			0.683888
$166$	5.49835	+	9.52343i	0.426755	+	0.739162i
$167$	−11.0042	+	19.0598i	−0.851529	+	1.47489i	0.0282996	+	0.999599i	$0.490991\pi$
$167$	−11.0042	+	19.0598i	−0.851529	+	1.47489i	−0.879828	+	0.475292i	$0.842343\pi$
$168$	−4.18111	+	7.24189i	−0.322579	+	0.558724i
$169$	−16.4703	+	28.5275i	−1.26695	+	2.19442i
$170$	4.50524	+	7.80330i	0.345536	+	0.598486i
$171$	−0.138606			−0.0105995
$172$	0.546953	+	0.947350i	0.0417047	+	0.0722347i
$173$	2.85296			0.216907			0.108453	−	0.994102i	$-0.465410\pi$
$173$	2.85296			0.216907			0.108453	+	0.994102i	$0.465410\pi$
$174$	−5.60916	+	9.71534i	−0.425229	+	0.736518i
$175$	−14.7792	−	25.5984i	−1.11720	−	1.93505i
$176$	2.97572	−	5.15409i	0.224303	−	0.388504i
$177$	2.15378	−	3.73045i	0.161888	−	0.280398i
$178$	−8.14760	+	14.1121i	−0.610688	+	1.05774i
$179$	4.75868	−	8.24228i	0.355681	−	0.616057i	−0.631553	−	0.775332i	$-0.717582\pi$
$179$	4.75868	−	8.24228i	0.355681	−	0.616057i	0.987234	+	0.159275i	$0.0509157\pi$
$180$	−2.06098			−0.153617
$181$	−5.17935	+	8.97090i	−0.384978	+	0.666801i	−0.991766	−	0.128062i	$-0.959124\pi$
$181$	−5.17935	+	8.97090i	−0.384978	+	0.666801i	0.606788	+	0.794864i	$0.292458\pi$
$182$	−11.2551	−	19.4943i	−0.834281	−	1.44502i
$183$	−3.04830	−	5.27981i	−0.225337	−	0.390295i
$184$	−1.47243			−0.108549
$185$	−16.9379			−1.24530
$186$	−12.8981			−0.945732
$187$	−2.05298	−	3.55586i	−0.150129	−	0.260030i
$188$	0.172797	+	0.299293i	0.0126025	+	0.0218282i
$189$	2.72799			0.198432
$190$	−0.335738	−	0.581515i	−0.0243570	−	0.0421875i
$191$	−7.60474	+	13.1718i	−0.550260	+	0.953078i	0.447996	+	0.894036i	$0.352138\pi$
$191$	−7.60474	+	13.1718i	−0.550260	+	0.953078i	−0.998255	+	0.0590422i	$0.981195\pi$
$192$	−4.42989	+	7.67280i	−0.319700	+	0.553737i
$193$	1.62910	+	2.82169i	0.117265	+	0.203110i	0.918683	−	0.394996i	$-0.129254\pi$
$193$	1.62910	+	2.82169i	0.117265	+	0.203110i	−0.801418	+	0.598105i	$0.795921\pi$
$194$	4.77262	+	8.26642i	0.342654	+	0.593494i
$195$	13.4859	−	23.3583i	0.965748	−	1.67272i
$196$	−0.228896			−0.0163497
$197$	4.64018	−	8.03703i	0.330599	−	0.572615i	−0.652030	−	0.758193i	$-0.726082\pi$
$197$	4.64018	−	8.03703i	0.330599	−	0.572615i	0.982630	+	0.185578i	$0.0594158\pi$
$198$	−2.68751			−0.190993
$199$	−2.49478	+	4.32109i	−0.176850	+	0.306314i	−0.940800	−	0.338962i	$-0.889924\pi$
$199$	−2.49478	+	4.32109i	−0.176850	+	0.306314i	0.763950	+	0.645276i	$0.223258\pi$
$200$	−16.6068	−	28.7638i	−1.17428	−	2.03391i
$201$	0.982097	−	1.70104i	0.0692717	−	0.119982i
$202$	11.5014			0.809236
$203$	−25.1383			−1.76436
$204$	0.481651	+	0.834243i	0.0337223	+	0.0584087i
$205$	−23.5390	+	40.7708i	−1.64404	+	2.84755i
$206$	−20.7542			−1.44602
$207$	0.240175	+	0.415995i	0.0166933	+	0.0289137i
$208$	−9.13641	−	15.8247i	−0.633496	−	1.09725i
$209$	0.152991	+	0.264989i	0.0105826	+	0.0183297i
$210$	6.60787	+	11.4452i	0.455986	+	0.789792i
$211$	22.0718			1.51949			0.759743	−	0.650224i	$-0.225325\pi$
$211$	22.0718			1.51949			0.759743	+	0.650224i	$0.225325\pi$
$212$	−2.15254	−	3.72832i	−0.147837	−	0.256062i
$213$	−6.18083			−0.423503
$214$	4.09013	+	7.08432i	0.279596	+	0.484274i
$215$	8.40484			0.573205
$216$	3.06533			0.208570
$217$	−14.4511	−	25.0301i	−0.981008	−	1.69916i
$218$	9.78197	−	16.9429i	0.662518	−	1.14752i
$219$	0.613864	+	1.06324i	0.0414811	+	0.0718473i
$220$	2.27488	+	3.94021i	0.153373	+	0.265649i
$221$	−12.6066			−0.848013
$222$	5.18182			0.347781
$223$	5.87556	+	10.1768i	0.393457	+	0.681487i	0.992903	−	0.118928i	$-0.0379458\pi$
$223$	5.87556	+	10.1768i	0.393457	+	0.681487i	−0.599446	+	0.800415i	$0.704613\pi$
$224$	−7.77106			−0.519226
$225$	−5.41761	+	9.38358i	−0.361174	+	0.625572i
$226$	2.34837	−	4.06749i	0.156211	−	0.270565i
$227$	7.83625	−	13.5728i	0.520110	−	0.900857i	−0.479617	−	0.877478i	$-0.659224\pi$
$227$	7.83625	−	13.5728i	0.520110	−	0.900857i	0.999727	−	0.0233788i	$-0.00744238\pi$
$228$	−0.0358934	−	0.0621692i	−0.00237710	−	0.00411725i
$229$	−9.80557	−	16.9837i	−0.647970	−	1.12232i	−0.983607	−	0.180326i	$-0.942285\pi$
$229$	−9.80557	−	16.9837i	−0.647970	−	1.12232i	0.335637	−	0.941991i	$-0.391049\pi$
$230$	−1.16352	+	2.01528i	−0.0767206	+	0.132884i
$231$	−3.01112	−	5.21541i	−0.198117	−	0.343149i
$232$	−28.2468			−1.85449
$233$	2.71787	−	4.70749i	0.178054	−	0.308398i	−0.763160	−	0.646209i	$-0.776353\pi$
$233$	2.71787	−	4.70749i	0.178054	−	0.308398i	0.941214	+	0.337811i	$0.109687\pi$
$234$	−4.12577	+	7.14604i	−0.269710	+	0.467151i
$235$	2.65531			0.173213
$236$	2.23097			0.145224
$237$	−2.36235	+	4.09172i	−0.153451	+	0.265786i
$238$	3.08851	−	5.34946i	0.200198	−	0.346754i
$239$	27.8817			1.80352			0.901759	−	0.432239i	$-0.142276\pi$
$239$	27.8817			1.80352			0.901759	+	0.432239i	$0.142276\pi$
$240$	5.36401	+	9.29073i	0.346245	+	0.599714i
$241$	−13.1960	+	22.8562i	−0.850030	+	1.47229i	0.0311510	+	0.999515i	$0.490083\pi$
$241$	−13.1960	+	22.8562i	−0.850030	+	1.47229i	−0.881181	+	0.472780i	$0.843251\pi$
$242$	−3.72930	−	6.45934i	−0.239729	−	0.415222i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	1.57878	−	2.73452i	0.101071	−	0.175060i
$245$	−0.879341	+	1.52306i	−0.0561790	+	0.0973049i
$246$	7.20132	−	12.4730i	0.459139	−	0.795252i
$247$	0.939466			0.0597768
$248$	−16.2382	−	28.1253i	−1.03112	−	1.78596i
$249$	9.03289			0.572436
$250$	−28.2687			−1.78787
$251$	2.83327	+	4.90737i	0.178834	+	0.309750i	0.941482	−	0.337064i	$-0.109434\pi$
$251$	2.83327	+	4.90737i	0.178834	+	0.309750i	−0.762647	+	0.646815i	$0.776101\pi$
$252$	0.706441	+	1.22359i	0.0445016	+	0.0770790i
$253$	0.530203	−	0.918339i	0.0333336	−	0.0577355i
$254$	−2.24189	−	3.88307i	−0.140669	−	0.243645i
$255$	7.40137			0.463492
$256$	−11.5246			−0.720285
$257$	−0.394804	−	0.683820i	−0.0246272	−	0.0426555i	0.853449	−	0.521176i	$-0.174507\pi$
$257$	−0.394804	−	0.683820i	−0.0246272	−	0.0426555i	−0.878076	+	0.478521i	$0.841173\pi$
$258$	−2.57130			−0.160082
$259$	5.80577	+	10.0559i	0.360753	+	0.624843i
$260$	13.9693			0.866336
$261$	4.60746	+	7.98036i	0.285195	+	0.493972i
$262$	4.55444	+	7.88853i	0.281374	+	0.487355i
$263$	12.8750	+	22.3001i	0.793905	+	1.37508i	0.923532	+	0.383522i	$0.125289\pi$
$263$	12.8750	+	22.3001i	0.793905	+	1.37508i	−0.129626	+	0.991563i	$0.541378\pi$
$264$	−3.38347	−	5.86034i	−0.208238	−	0.360679i
$265$	−33.0774			−2.03193
$266$	−0.230161	+	0.398650i	−0.0141121	+	0.0244428i
$267$	6.69258	+	11.5919i	0.409579	+	0.709413i
$268$	1.01729			0.0621411
$269$	−3.79898			−0.231628			−0.115814	−	0.993271i	$-0.536948\pi$
$269$	−3.79898			−0.231628			−0.115814	+	0.993271i	$0.536948\pi$
$270$	2.42225	−	4.19545i	0.147413	−	0.255327i
$271$	3.93983	+	6.82399i	0.239328	+	0.414528i	0.960522	−	0.278206i	$-0.0897397\pi$
$271$	3.93983	+	6.82399i	0.239328	+	0.414528i	−0.721194	+	0.692733i	$0.756406\pi$
$272$	2.50713	−	4.34248i	0.152017	−	0.263301i
$273$	−18.4902			−1.11908
$274$	−5.70269	+	9.87735i	−0.344512	+	0.596712i
$275$	23.9195			1.44240
$276$	−0.124391	+	0.215452i	−0.00748747	+	0.0129687i
$277$	−8.57928	−	14.8598i	−0.515479	−	0.892836i	−0.999839	−	0.0179669i	$-0.994281\pi$
$277$	−8.57928	−	14.8598i	−0.515479	−	0.892836i	0.484360	−	0.874869i	$-0.339053\pi$
$278$	−8.16485	−	14.1419i	−0.489695	−	0.848176i
$279$	−5.29735	+	9.17528i	−0.317144	+	0.549310i
$280$	−16.6381	+	28.8180i	−0.994316	+	1.72221i
$281$	6.32771	+	10.9599i	0.377479	+	0.653814i	0.990695	−	0.136102i	$-0.0434576\pi$
$281$	6.32771	+	10.9599i	0.377479	+	0.653814i	−0.613215	+	0.789916i	$0.710124\pi$
$282$	−0.812343			−0.0483743
$283$	7.49152	+	12.9757i	0.445325	+	0.771325i	0.998075	−	0.0620222i	$-0.0197550\pi$
$283$	7.49152	+	12.9757i	0.445325	+	0.771325i	−0.552750	+	0.833347i	$0.686422\pi$
$284$	−1.60059	−	2.77230i	−0.0949773	−	0.164506i
$285$	−0.551562			−0.0326717
$286$	18.2158			1.07713
$287$	32.2738			1.90506
$288$	1.42432	+	2.46699i	0.0839287	+	0.145369i
$289$	6.77030	+	11.7265i	0.398253	+	0.689795i
$290$	−22.3208	+	38.6608i	−1.31072	+	2.27024i
$291$	7.84063			0.459626
$292$	−0.317932	+	0.550674i	−0.0186056	+	0.0322258i
$293$	−15.9600	+	27.6436i	−0.932396	+	1.61496i	−0.153182	+	0.988198i	$0.548952\pi$
$293$	−15.9600	+	27.6436i	−0.932396	+	1.61496i	−0.779214	+	0.626758i	$0.784381\pi$
$294$	0.269018	−	0.465953i	0.0156894	−	0.0271749i
$295$	8.57064	−	14.8448i	0.499002	−	0.864297i
$296$	6.52371	+	11.2994i	0.379183	+	0.656764i
$297$	−1.10379	+	1.91181i	−0.0640481	+	0.110935i
$298$	−2.44097			−0.141401
$299$	−1.62789	−	2.81960i	−0.0941436	−	0.163061i
$300$	−5.61178			−0.323996
$301$	−2.88092	−	4.98989i	−0.166053	−	0.287613i
$302$	−2.15179	+	3.72700i	−0.123821	+	0.214465i
$303$	4.72373	−	8.18174i	0.271371	−	0.470028i
$304$	−0.186835	+	0.323608i	−0.0107157	+	0.0185602i
$305$	−12.1303	−	21.0102i	−0.694577	−	1.20304i
$306$	−2.26431			−0.129442
$307$	19.3563			1.10472			0.552360	−	0.833605i	$-0.313727\pi$
$307$	19.3563			1.10472			0.552360	+	0.833605i	$0.313727\pi$
$308$	1.55952	−	2.70116i	0.0888618	−	0.153913i
$309$	−8.52394	+	14.7639i	−0.484910	+	0.839889i
$310$	−51.3259			−2.91512
$311$	12.1814	−	21.0989i	0.690746	−	1.19641i	−0.280847	−	0.959752i	$-0.590615\pi$
$311$	12.1814	−	21.0989i	0.690746	−	1.19641i	0.971594	−	0.236655i	$-0.0760512\pi$
$312$	−20.7767			−1.17625
$313$	1.96038			0.110807			0.0554035	−	0.998464i	$-0.482355\pi$
$313$	1.96038			0.110807			0.0554035	+	0.998464i	$0.482355\pi$
$314$	11.1837	+	10.3735i	0.631135	+	0.585413i
$315$	10.8556			0.611646
$316$	−2.44702			−0.137656
$317$	−0.975394	+	1.68943i	−0.0547836	+	0.0948880i	−0.892117	−	0.451805i	$-0.850780\pi$
$317$	−0.975394	+	1.68943i	−0.0547836	+	0.0948880i	0.837333	+	0.546693i	$0.184114\pi$
$318$	10.1194			0.567469
$319$	10.1713	−	17.6172i	0.569483	−	0.986374i
$320$	−17.6281	+	30.5328i	−0.985441	+	1.70683i
$321$	6.71942			0.375041
$322$	1.59528			0.0889015
$323$	0.128900	+	0.223261i	0.00717217	+	0.0124226i
$324$	0.258960	−	0.448531i	0.0143867	−	0.0249184i
$325$	36.7204	−	63.6015i	2.03688	−	3.52798i
$326$	9.84030	−	17.0439i	0.545004	−	0.943974i
$327$	−8.03508	−	13.9172i	−0.444341	−	0.769621i
$328$	36.2647			2.00238
$329$	−0.910158	−	1.57644i	−0.0501787	−	0.0869120i
$330$	−10.6946			−0.588716
$331$	1.19158	−	2.06387i	0.0654950	−	0.113441i	−0.831418	−	0.555647i	$-0.812471\pi$
$331$	1.19158	−	2.06387i	0.0654950	−	0.113441i	0.896913	+	0.442206i	$0.145804\pi$
$332$	2.33916	+	4.05154i	0.128378	+	0.222357i
$333$	2.12822	−	3.68619i	0.116626	−	0.202002i
$334$	13.3966	−	23.2035i	0.733027	−	1.26964i
$335$	3.90811	−	6.76904i	0.213523	−	0.369832i
$336$	3.67723	−	6.36914i	0.200609	−	0.347465i
$337$	−32.4150			−1.76576			−0.882879	−	0.469600i	$-0.844398\pi$
$337$	−32.4150			−1.76576			−0.882879	+	0.469600i	$0.844398\pi$
$338$	20.0511	−	34.7295i	1.09064	−	1.88904i
$339$	−1.92899	−	3.34111i	−0.104768	−	0.181464i
$340$	1.91666	+	3.31975i	0.103945	+	0.180039i
$341$	23.3886			1.26656
$342$	0.168740			0.00912442
$343$	−17.8903			−0.965986
$344$	−3.23717	−	5.60694i	−0.174536	−	0.302306i
$345$	0.955740	+	1.65539i	0.0514553	+	0.0891232i
$346$	−3.47322			−0.186721
$347$	−11.9504	−	20.6987i	−0.641532	−	1.11117i	−0.985091	−	0.172035i	$-0.944966\pi$
$347$	−11.9504	−	20.6987i	−0.641532	−	1.11117i	0.343558	−	0.939131i	$-0.388368\pi$
$348$	−2.38629	+	4.13318i	−0.127919	+	0.221562i
$349$	−1.34647	+	2.33215i	−0.0720747	+	0.124837i	−0.899810	−	0.436281i	$-0.856295\pi$
$349$	−1.34647	+	2.33215i	−0.0720747	+	0.124837i	0.827736	+	0.561118i	$0.189629\pi$
$350$	17.9923	+	31.1636i	0.961731	+	1.66577i
$351$	3.38898	+	5.86988i	0.180890	+	0.313311i
$352$	3.14428	−	5.44605i	0.167591	−	0.290276i
$353$	2.32010			0.123487			0.0617433	−	0.998092i	$-0.480334\pi$
$353$	2.32010			0.123487			0.0617433	+	0.998092i	$0.480334\pi$
$354$	−2.62203	+	4.54148i	−0.139359	+	0.241377i
$355$	−24.5957			−1.30540
$356$	−3.46622	+	6.00367i	−0.183709	+	0.318194i
$357$	−2.53696	−	4.39414i	−0.134270	−	0.232563i
$358$	−5.79326	+	10.0342i	−0.306183	+	0.530325i
$359$	−32.6628			−1.72388			−0.861939	−	0.507011i	$-0.830750\pi$
$359$	−32.6628			−1.72388			−0.861939	+	0.507011i	$0.830750\pi$
$360$	12.1980			0.642893
$361$	9.49039	+	16.4378i	0.499494	+	0.865150i
$362$	6.30538	−	10.9212i	0.331403	−	0.574007i
$363$	−6.12663			−0.321565
$364$	−4.78822	−	8.29345i	−0.250971	−	0.434695i
$365$	2.44278	+	4.23102i	0.127861	+	0.221461i
$366$	3.71103	+	6.42768i	0.193978	+	0.335980i
$367$	5.43150	+	9.40763i	0.283522	+	0.491074i	0.972250	−	0.233946i	$-0.0751638\pi$
$367$	5.43150	+	9.40763i	0.283522	+	0.491074i	−0.688728	+	0.725020i	$0.741831\pi$
$368$	1.29498			0.0675057
$369$	−5.91529	−	10.2456i	−0.307938	−	0.533364i
$370$	20.6203			1.07200
$371$	11.3379	+	19.6378i	0.588635	+	1.01955i
$372$	−5.48720			−0.284498
$373$	28.0810			1.45398			0.726990	−	0.686648i	$-0.240918\pi$
$373$	28.0810			1.45398			0.726990	+	0.686648i	$0.240918\pi$
$374$	2.49931	+	4.32893i	0.129236	+	0.223844i
$375$	−11.6102	+	20.1095i	−0.599549	+	1.03845i
$376$	−1.02271	−	1.77138i	−0.0527421	−	0.0913520i
$377$	−31.2292	−	54.0905i	−1.60838	−	2.78580i
$378$	−3.32108			−0.170818
$379$	24.7108			1.26931			0.634655	−	0.772795i	$-0.281142\pi$
$379$	24.7108			1.26931			0.634655	+	0.772795i	$0.281142\pi$
$380$	−0.142832	−	0.247393i	−0.00732715	−	0.0126910i
$381$	−3.68306			−0.188689
$382$	9.25807	−	16.0354i	0.473684	−	0.820445i
$383$	−9.28417	+	16.0807i	−0.474399	+	0.821683i	−0.999570	−	0.0293133i	$-0.990668\pi$
$383$	−9.28417	+	16.0807i	−0.474399	+	0.821683i	0.525171	+	0.850997i	$0.324001\pi$
$384$	2.54435	−	4.40695i	0.129841	−	0.224891i
$385$	−11.9823	−	20.7540i	−0.610675	−	1.05772i
$386$	−1.98328	−	3.43514i	−0.100946	−	0.174844i
$387$	−1.05606	+	1.82914i	−0.0536824	+	0.0929806i
$388$	2.03041	+	3.51677i	0.103078	+	0.178537i
$389$	32.2402			1.63464			0.817322	−	0.576181i	$-0.195458\pi$
$389$	32.2402			1.63464			0.817322	+	0.576181i	$0.195458\pi$
$390$	−16.4179	+	28.4366i	−0.831351	+	1.43994i
$391$	0.446712	−	0.773727i	0.0225912	−	0.0391291i
$392$	1.35473			0.0684242
$393$	7.48220			0.377427
$394$	−5.64899	+	9.78434i	−0.284592	+	0.492928i
$395$	−9.40064	+	16.2824i	−0.472997	+	0.819255i
$396$	−1.14334			−0.0574552
$397$	2.46966	+	4.27757i	0.123949	+	0.214685i	0.921321	−	0.388802i	$-0.127111\pi$
$397$	2.46966	+	4.27757i	0.123949	+	0.214685i	−0.797373	+	0.603487i	$0.793778\pi$
$398$	3.03717	−	5.26053i	0.152239	−	0.263686i
$399$	0.189058	+	0.327458i	0.00946475	+	0.0163934i
$400$	14.6055	+	25.2974i	0.730273	+	1.26487i
$401$	−6.91450	+	11.9763i	−0.345293	+	0.598066i	−0.985407	−	0.170214i	$-0.945554\pi$
$401$	−6.91450	+	11.9763i	−0.345293	+	0.598066i	0.640114	+	0.768280i	$0.278887\pi$
$402$	−1.19561	+	2.07086i	−0.0596317	+	0.103285i
$403$	35.9052	−	62.1897i	1.78857	−	3.09789i
$404$	4.89302			0.243437
$405$	−1.98968	−	3.44622i	−0.0988678	−	0.171244i
$406$	30.6035			1.51883
$407$	−9.39640			−0.465762
$408$	−2.85067	−	4.93751i	−0.141129	−	0.244443i
$409$	−3.14345	−	5.44462i	−0.155434	−	0.269219i	0.777783	−	0.628533i	$-0.216344\pi$
$409$	−3.14345	−	5.44462i	−0.155434	−	0.269219i	−0.933217	+	0.359314i	$0.883011\pi$
$410$	28.6566	−	49.6346i	1.41525	−	2.45128i
$411$	4.68429	+	8.11343i	0.231059	+	0.400206i
$412$	−8.82943			−0.434995
$413$	−11.7510			−0.578228
$414$	−0.292391	−	0.506435i	−0.0143702	−	0.0248899i
$415$	35.9450			1.76447
$416$	−9.65396	−	16.7211i	−0.473324	−	0.819822i
$417$	−13.4135			−0.656862
$418$	−0.186253	−	0.322599i	−0.00910992	−	0.0157788i
$419$	1.99005	+	3.44687i	0.0972204	+	0.168391i	0.910533	−	0.413436i	$-0.135671\pi$
$419$	1.99005	+	3.44687i	0.0972204	+	0.168391i	−0.813313	+	0.581827i	$0.802338\pi$
$420$	2.81118	+	4.86910i	0.137171	+	0.237588i
$421$	1.85955	+	3.22083i	0.0906287	+	0.156974i	0.907776	−	0.419456i	$-0.137779\pi$
$421$	1.85955	+	3.22083i	0.0906287	+	0.156974i	−0.817147	+	0.576429i	$0.804446\pi$
$422$	−26.8704			−1.30803
$423$	−0.333636	+	0.577875i	−0.0162220	+	0.0280973i
$424$	12.7399	+	22.0662i	0.618706	+	1.07163i
$425$	20.1529			0.977560
$426$	7.52459			0.364567
$427$	−8.31575	+	14.4033i	−0.402427	+	0.697025i
$428$	1.74006	+	3.01387i	0.0841089	+	0.145681i
$429$	7.48141	−	12.9582i	0.361206	−	0.625627i
$430$	−10.2321			−0.493436
$431$	0.548337	−	0.949748i	0.0264125	−	0.0457477i	−0.852517	−	0.522699i	$-0.824925\pi$
$431$	0.548337	−	0.949748i	0.0264125	−	0.0457477i	0.878930	+	0.476952i	$0.158258\pi$
$432$	−2.69592			−0.129708
$433$	4.24618	−	7.35460i	0.204059	−	0.353440i	−0.745774	−	0.666199i	$-0.767920\pi$
$433$	4.24618	−	7.35460i	0.204059	−	0.353440i	0.949832	+	0.312759i	$0.101253\pi$
$434$	17.5929	+	30.4719i	0.844488	+	1.46270i
$435$	18.3347	+	31.7566i	0.879082	+	1.52261i
$436$	4.16153	−	7.20797i	0.199301	−	0.345199i
$437$	−0.0332897	+	0.0576594i	−0.00159246	+	0.00275823i
$438$	−0.747322	−	1.29440i	−0.0357084	−	0.0618488i
$439$	14.9677			0.714370			0.357185	−	0.934034i	$-0.383737\pi$
$439$	14.9677			0.714370			0.357185	+	0.934034i	$0.383737\pi$
$440$	−13.4640	−	23.3204i	−0.641872	−	1.11175i
$441$	−0.220976	−	0.382742i	−0.0105227	−	0.0182258i
$442$	15.3474			0.730001
$443$	−1.58356			−0.0752371			−0.0376186	−	0.999292i	$-0.511977\pi$
$443$	−1.58356			−0.0752371			−0.0376186	+	0.999292i	$0.511977\pi$
$444$	2.20449			0.104621
$445$	26.6321	+	46.1282i	1.26248	+	2.18669i
$446$	−7.15295	−	12.3893i	−0.338702	−	0.586649i
$447$	−1.00253	+	1.73643i	−0.0474179	+	0.0821302i
$448$	24.1695			1.14190
$449$	−3.38797	+	5.86813i	−0.159888	+	0.276934i	−0.934828	−	0.355100i	$-0.884447\pi$
$449$	−3.38797	+	5.86813i	−0.159888	+	0.276934i	0.774940	+	0.632035i	$0.217780\pi$
$450$	6.59544	−	11.4236i	0.310912	−	0.538516i
$451$	−13.0584	+	22.6178i	−0.614897	+	1.06503i
$452$	0.999061	−	1.73042i	0.0469919	−	0.0813923i
$453$	1.76752	+	3.06143i	0.0830451	+	0.143838i
$454$	−9.53990	+	16.5236i	−0.447730	+	0.775491i
$455$	−73.5791			−3.44944
$456$	0.212437	+	0.367951i	0.00994827	+	0.0172309i
$457$	−22.3740			−1.04661			−0.523306	−	0.852145i	$-0.675301\pi$
$457$	−22.3740			−1.04661			−0.523306	+	0.852145i	$0.675301\pi$
$458$	11.9374	+	20.6761i	0.557797	+	0.966132i
$459$	−0.929972	+	1.61076i	−0.0434074	+	0.0751838i
$460$	−0.494996	+	0.857359i	−0.0230793	+	0.0399746i
$461$	8.34653	−	14.4566i	0.388737	−	0.673312i	−0.603543	−	0.797330i	$-0.706245\pi$
$461$	8.34653	−	14.4566i	0.388737	−	0.673312i	0.992280	+	0.124019i	$0.0395783\pi$
$462$	3.66576	+	6.34928i	0.170547	+	0.295395i
$463$	36.9510			1.71726			0.858630	−	0.512596i	$-0.171316\pi$
$463$	36.9510			1.71726			0.858630	+	0.512596i	$0.171316\pi$
$464$	24.8427			1.15329
$465$	−21.0800	+	36.5117i	−0.977563	+	1.69319i
$466$	−3.30876	+	5.73093i	−0.153275	+	0.265480i
$467$	20.5231			0.949697			0.474849	−	0.880068i	$-0.342503\pi$
$467$	20.5231			0.949697			0.474849	+	0.880068i	$0.342503\pi$
$468$	−1.75522	+	3.04013i	−0.0811350	+	0.140530i
$469$	−5.35831			−0.247424
$470$	−3.23260			−0.149109
$471$	11.9727	−	3.69526i	0.551672	−	0.170269i
$472$	−13.2041			−0.607768
$473$	4.66264			0.214388
$474$	2.87595	−	4.98129i	0.132097	−	0.228798i
$475$	−1.50183			−0.0689086
$476$	1.31394	−	2.27581i	0.0602243	−	0.104312i
$477$	4.15614	−	7.19864i	0.190296	−	0.329603i
$478$	−33.9434			−1.55253
$479$	−7.74311			−0.353792			−0.176896	−	0.984230i	$-0.556606\pi$
$479$	−7.74311			−0.353792			−0.176896	+	0.984230i	$0.556606\pi$
$480$	5.66786	+	9.81702i	0.258701	+	0.448083i
$481$	−14.4250	+	24.9848i	−0.657723	+	1.13921i
$482$	16.0649	−	27.8253i	0.731737	−	1.26741i
$483$	0.655196	−	1.13483i	0.0298124	−	0.0516367i
$484$	−1.58655	−	2.74799i	−0.0721160	−	0.124909i
$485$	31.2006			1.41675
$486$	0.608704	+	1.05431i	0.0276114	+	0.0478243i
$487$	−13.6288			−0.617581			−0.308791	−	0.951130i	$-0.599924\pi$
$487$	−13.6288			−0.617581			−0.308791	+	0.951130i	$0.599924\pi$
$488$	−9.34406	+	16.1844i	−0.422986	+	0.732633i
$489$	−8.08299	−	14.0002i	−0.365526	−	0.633109i
$490$	1.07052	−	1.85419i	0.0483610	−	0.0837637i
$491$	−15.1176	+	26.1844i	−0.682246	+	1.18169i	0.292048	+	0.956404i	$0.405663\pi$
$491$	−15.1176	+	26.1844i	−0.682246	+	1.18169i	−0.974294	+	0.225281i	$0.927670\pi$
$492$	3.06364	−	5.30639i	0.138120	−	0.239230i
$493$	8.56962	−	14.8430i	0.385956	−	0.668496i
$494$	−1.14371			−0.0514581
$495$	−4.39235	+	7.60777i	−0.197421	+	0.341944i
$496$	14.2812	+	24.7358i	0.641247	+	1.11067i
$497$	8.43063	+	14.6023i	0.378166	+	0.655002i
$498$	−10.9967			−0.492774
$499$	−11.8729			−0.531505			−0.265753	−	0.964041i	$-0.585620\pi$
$499$	−11.8729			−0.531505			−0.265753	+	0.964041i	$0.585620\pi$
$500$	−12.0263			−0.537833
$501$	−11.0042	−	19.0598i	−0.491630	−	0.851529i
$502$	−3.44924	−	5.97426i	−0.153947	−	0.266644i
$503$	1.44794			0.0645606			0.0322803	−	0.999479i	$-0.489723\pi$
$503$	1.44794			0.0645606			0.0322803	+	0.999479i	$0.489723\pi$
$504$	−4.18111	−	7.24189i	−0.186241	−	0.322579i
$505$	18.7974	−	32.5580i	0.836472	−	1.44881i
$506$	−0.645473	+	1.11799i	−0.0286948	+	0.0497008i
$507$	−16.4703	−	28.5275i	−0.731474	−	1.26695i
$508$	−0.953764	−	1.65197i	−0.0423164	−	0.0732942i
$509$	15.0164	−	26.0091i	0.665590	−	1.15284i	−0.313535	−	0.949577i	$-0.601513\pi$
$509$	15.0164	−	26.0091i	0.665590	−	1.15284i	0.979125	−	0.203259i	$-0.0651532\pi$
$510$	−9.01048			−0.398991
$511$	1.67462	−	2.90052i	0.0740807	−	0.128311i
$512$	24.2075			1.06983
$513$	0.0693030	−	0.120036i	0.00305980	−	0.00529973i
$514$	0.480637	+	0.832487i	0.0212000	+	0.0367194i
$515$	−33.9198	+	58.7507i	−1.49468	+	2.58887i
$516$	−1.09391			−0.0481565
$517$	1.47305			0.0647848
$518$	−7.06799	−	12.2421i	−0.310550	−	0.537888i
$519$	−1.42648	+	2.47074i	−0.0626156	+	0.108453i
$520$	−82.6777			−3.62566
$521$	13.7581	+	23.8297i	0.602751	+	1.04400i	0.992403	+	0.123034i	$0.0392623\pi$
$521$	13.7581	+	23.8297i	0.602751	+	1.04400i	−0.389651	+	0.920963i	$0.627404\pi$
$522$	−5.60916	−	9.71534i	−0.245506	−	0.425229i
$523$	5.79564	+	10.0383i	0.253426	+	0.438946i	0.964467	−	0.264204i	$-0.0851093\pi$
$523$	5.79564	+	10.0383i	0.253426	+	0.438946i	−0.711041	+	0.703150i	$0.751776\pi$
$524$	1.93759	+	3.35600i	0.0846440	+	0.146608i
$525$	29.5584			1.29004
$526$	−15.6741	−	27.1483i	−0.683423	−	1.18372i
$527$	19.7056			0.858387
$528$	2.97572	+	5.15409i	0.129501	+	0.224303i
$529$	−22.7693			−0.989968
$530$	40.2687			1.74916
$531$	2.15378	+	3.73045i	0.0934660	+	0.161888i
$532$	−0.0979170	+	0.169597i	−0.00424524	+	0.00735297i
$533$	40.0936	+	69.4441i	1.73665	+	3.00796i
$534$	−8.14760	−	14.1121i	−0.352581	−	0.610688i
$535$	26.7389			1.15602
$536$	−6.02091			−0.260064
$537$	4.75868	+	8.24228i	0.205352	+	0.355681i
$538$	4.62491			0.199394
$539$	−0.487820	+	0.844929i	−0.0210119	+	0.0363937i
$540$	1.03049	−	1.78486i	0.0443453	−	0.0768083i
$541$	−0.162796	+	0.281971i	−0.00699914	+	0.0121229i	−0.869504	−	0.493926i	$-0.835561\pi$
$541$	−0.162796	+	0.281971i	−0.00699914	+	0.0121229i	0.862505	+	0.506049i	$0.168895\pi$
$542$	−4.79638	−	8.30757i	−0.206022	−	0.356841i
$543$	−5.17935	−	8.97090i	−0.222267	−	0.384978i
$544$	2.64915	−	4.58846i	0.113581	−	0.196729i
$545$	−31.9744	−	55.3813i	−1.36963	−	2.37227i
$546$	22.5101			0.963345
$547$	2.87275	−	4.97574i	0.122830	−	0.212747i	−0.798053	−	0.602588i	$-0.794136\pi$
$547$	2.87275	−	4.97574i	0.122830	−	0.212747i	0.920883	+	0.389840i	$0.127470\pi$
$548$	−2.42608	+	4.20210i	−0.103637	+	0.179505i
$549$	6.09660			0.260197
$550$	−29.1198			−1.24167
$551$	−0.638622	+	1.10613i	−0.0272062	+	0.0471225i
$552$	0.736216	−	1.27516i	0.0313354	−	0.0542746i
$553$	12.8890			0.548095
$554$	10.4445	+	18.0904i	0.443743	+	0.768586i
$555$	8.46894	−	14.6686i	0.359486	−	0.622649i
$556$	−3.47356	−	6.01638i	−0.147312	−	0.255151i
$557$	0.771022	+	1.33545i	0.0326693	+	0.0565848i	0.881898	−	0.471441i	$-0.156266\pi$
$557$	0.771022	+	1.33545i	0.0326693	+	0.0565848i	−0.849229	+	0.528026i	$0.822933\pi$
$558$	6.44904	−	11.1701i	0.273009	−	0.472866i
$559$	7.15791	−	12.3979i	0.302747	−	0.524374i
$560$	14.6330	−	25.3451i	0.618356	−	1.07102i
$561$	4.10596			0.173354
$562$	−7.70340	−	13.3427i	−0.324948	−	0.562827i
$563$	−36.7271			−1.54786			−0.773932	−	0.633268i	$-0.781713\pi$
$563$	−36.7271			−1.54786			−0.773932	+	0.633268i	$0.781713\pi$
$564$	−0.345594			−0.0145521
$565$	−7.67612	−	13.2954i	−0.322937	−	0.559343i
$566$	−9.12023	−	15.7967i	−0.383352	−	0.663985i
$567$	−1.36400	+	2.36251i	−0.0572825	+	0.0992162i
$568$	9.47315	+	16.4080i	0.397485	+	0.688464i
$569$	−30.0907			−1.26147			−0.630734	−	0.775999i	$-0.717246\pi$
$569$	−30.0907			−1.26147			−0.630734	+	0.775999i	$0.717246\pi$
$570$	0.671476			0.0281250
$571$	−10.3054	−	17.8495i	−0.431267	−	0.746977i	0.565716	−	0.824600i	$-0.308600\pi$
$571$	−10.3054	−	17.8495i	−0.431267	−	0.746977i	−0.996983	+	0.0776239i	$0.975267\pi$
$572$	7.74954			0.324024
$573$	−7.60474	−	13.1718i	−0.317693	−	0.550260i
$574$	−39.2903			−1.63995
$575$	2.60235	+	4.50740i	0.108525	+	0.187972i
$576$	−4.42989	−	7.67280i	−0.184579	−	0.319700i
$577$	1.94348	+	3.36621i	0.0809083	+	0.140137i	0.903640	−	0.428292i	$-0.140885\pi$
$577$	1.94348	+	3.36621i	0.0809083	+	0.140137i	−0.822732	+	0.568429i	$0.807551\pi$
$578$	−8.24222	−	14.2759i	−0.342831	−	0.593801i
$579$	−3.25820			−0.135406
$580$	−9.49590	+	16.4474i	−0.394296	+	0.682940i
$581$	−12.3208	−	21.3403i	−0.511155	−	0.885346i
$582$	−9.54524			−0.395663
$583$	−18.3499			−0.759976
$584$	1.88170	−	3.25919i	0.0778652	−	0.134866i
$585$	13.4859	+	23.3583i	0.557575	+	0.965748i
$586$	19.4299	−	33.6535i	0.802641	−	1.39021i
$587$	32.9033			1.35806			0.679031	−	0.734109i	$-0.262400\pi$
$587$	32.9033			1.35806			0.679031	+	0.734109i	$0.262400\pi$
$588$	0.114448	−	0.198229i	0.00471975	−	0.00817484i
$589$	−1.46849			−0.0605081
$590$	−10.4340	+	18.0721i	−0.429559	+	0.744018i
$591$	4.64018	+	8.03703i	0.190872	+	0.330599i
$592$	−5.73751	−	9.93766i	−0.235810	−	0.408436i
$593$	3.88076	−	6.72168i	0.159364	−	0.276026i	−0.775276	−	0.631623i	$-0.782389\pi$
$593$	3.88076	−	6.72168i	0.159364	−	0.276026i	0.934639	+	0.355597i	$0.115722\pi$
$594$	1.34376	−	2.32745i	0.0551350	−	0.0954966i
$595$	−10.0954	−	17.4858i	−0.413873	−	0.716849i
$596$	−1.03846			−0.0425368
$597$	−2.49478	−	4.32109i	−0.102105	−	0.176850i
$598$	1.98181	+	3.43260i	0.0810423	+	0.140369i
$599$	35.1519			1.43627			0.718134	−	0.695905i	$-0.244997\pi$
$599$	35.1519			1.43627			0.718134	+	0.695905i	$0.244997\pi$
$600$	33.2136			1.35594
$601$	1.49919			0.0611532			0.0305766	−	0.999532i	$-0.490266\pi$
$601$	1.49919			0.0611532			0.0305766	+	0.999532i	$0.490266\pi$
$602$	3.50725	+	6.07473i	0.142945	+	0.247588i
$603$	0.982097	+	1.70104i	0.0399941	+	0.0692717i
$604$	−0.915431	+	1.58557i	−0.0372483	+	0.0645160i
$605$	−24.3800			−0.991188
$606$	−5.75070	+	9.96051i	−0.233606	+	0.404618i
$607$	−3.96091	+	6.86050i	−0.160768	+	0.278459i	−0.935144	−	0.354267i	$-0.884731\pi$
$607$	−3.96091	+	6.86050i	−0.160768	+	0.278459i	0.774376	+	0.632726i	$0.218064\pi$
$608$	−0.197419	+	0.341940i	−0.00800640	+	0.0138675i
$609$	12.5691	−	21.7704i	0.509327	−	0.882180i
$610$	14.7675	+	25.5780i	0.597917	+	1.03562i
$611$	2.26137	−	3.91681i	0.0914854	−	0.158457i
$612$	−0.963301			−0.0389391
$613$	18.4130	+	31.8923i	0.743696	+	1.28812i	0.950802	+	0.309800i	$0.100262\pi$
$613$	18.4130	+	31.8923i	0.743696	+	1.28812i	−0.207106	+	0.978318i	$0.566405\pi$
$614$	−23.5645			−0.950985
$615$	−23.5390	−	40.7708i	−0.949184	−	1.64404i
$616$	−9.23009	+	15.9870i	−0.371891	+	0.644134i
$617$	10.0324	−	17.3767i	0.403891	−	0.699559i	−0.590301	−	0.807183i	$-0.700991\pi$
$617$	10.0324	−	17.3767i	0.403891	−	0.699559i	0.994192	+	0.107624i	$0.0343243\pi$
$618$	10.3771	−	17.9737i	0.417429	−	0.723008i
$619$	−1.77797	−	3.07954i	−0.0714627	−	0.123777i	0.828080	−	0.560610i	$-0.189433\pi$
$619$	−1.77797	−	3.07954i	−0.0714627	−	0.123777i	−0.899543	+	0.436833i	$0.856100\pi$
$620$	−21.8355			−0.876935
$621$	−0.480350			−0.0192758
$622$	−14.8298	+	25.6859i	−0.594620	+	1.02991i
$623$	18.2573	−	31.6226i	0.731464	−	1.26693i
$624$	18.2728			0.731499
$625$	−19.1130	+	33.1047i	−0.764521	+	1.32419i
$626$	−2.38658			−0.0953867
$627$	−0.305983			−0.0122198
$628$	4.75788	+	4.41320i	0.189860	+	0.176106i
$629$	−7.91674			−0.315661
$630$	−13.2157			−0.526528
$631$	−14.5434	+	25.1900i	−0.578965	+	1.00280i	0.416634	+	0.909074i	$0.363210\pi$
$631$	−14.5434	+	25.1900i	−0.578965	+	1.00280i	−0.995598	+	0.0937217i	$0.970124\pi$
$632$	14.4828			0.576095
$633$	−11.0359	+	19.1147i	−0.438638	+	0.759743i
$634$	1.18745	−	2.05673i	0.0471597	−	0.0816831i
$635$	−14.6562			−0.581613
$636$	4.30509			0.170708
$637$	1.49777	+	2.59421i	0.0593436	+	0.102786i
$638$	−12.3826	+	21.4473i	−0.490232	+	0.849107i
$639$	3.09041	−	5.35276i	0.122255	−	0.211752i
$640$	10.1249	−	17.5368i	0.400220	−	0.693202i
$641$	8.78362	+	15.2137i	0.346932	+	0.600904i	0.985703	−	0.168493i	$-0.0538900\pi$
$641$	8.78362	+	15.2137i	0.346932	+	0.600904i	−0.638771	+	0.769397i	$0.720557\pi$
$642$	−8.18027			−0.322849
$643$	−10.1135	−	17.5171i	−0.398838	−	0.690807i	0.594745	−	0.803914i	$-0.297253\pi$
$643$	−10.1135	−	17.5171i	−0.398838	−	0.690807i	−0.993583	+	0.113107i	$0.963920\pi$
$644$	0.678677			0.0267436
$645$	−4.20242	+	7.27881i	−0.165470	+	0.286603i
$646$	−0.156923	−	0.271799i	−0.00617407	−	0.0106938i
$647$	−8.98643	+	15.5650i	−0.353293	+	0.611921i	−0.986824	−	0.161796i	$-0.948271\pi$
$647$	−8.98643	+	15.5650i	−0.353293	+	0.611921i	0.633531	+	0.773717i	$0.281605\pi$
$648$	−1.53267	+	2.65466i	−0.0602088	+	0.104285i
$649$	4.75462	−	8.23524i	0.186635	−	0.323261i
$650$	−44.7036	+	77.4289i	−1.75342	+	3.03701i
$651$	28.9023			1.13277
$652$	4.18634	−	7.25095i	0.163950	−	0.283969i
$653$	−20.5314	−	35.5614i	−0.803454	−	1.39162i	−0.917330	−	0.398129i	$-0.869660\pi$
$653$	−20.5314	−	35.5614i	−0.803454	−	1.39162i	0.113875	−	0.993495i	$-0.463674\pi$
$654$	9.78197	+	16.9429i	0.382505	+	0.662518i
$655$	29.7743			1.16338
$656$	−31.8943			−1.24526
$657$	−1.22773			−0.0478982
$658$	1.10803	+	1.91917i	0.0431956	+	0.0748170i
$659$	−14.5291	−	25.1651i	−0.565973	−	0.980295i	−0.996958	−	0.0779355i	$-0.975167\pi$
$659$	−14.5291	−	25.1651i	−0.565973	−	0.980295i	0.430985	−	0.902359i	$-0.358166\pi$
$660$	−4.54977			−0.177099
$661$	−4.11151	−	7.12135i	−0.159919	−	0.276988i	0.774920	−	0.632059i	$-0.217790\pi$
$661$	−4.11151	−	7.12135i	−0.159919	−	0.276988i	−0.934839	+	0.355071i	$0.884457\pi$
$662$	−1.45063	+	2.51257i	−0.0563805	+	0.0976539i
$663$	6.30331	−	10.9177i	0.244800	−	0.424006i
$664$	−13.8444	−	23.9792i	−0.537267	−	0.930575i
$665$	0.752329	+	1.30307i	0.0291741	+	0.0505310i
$666$	−2.59091	+	4.48759i	−0.100396	+	0.173891i
$667$	4.42639			0.171390
$668$	5.69928	−	9.87144i	0.220512	−	0.381937i
$669$	−11.7511			−0.454325
$670$	−4.75776	+	8.24068i	−0.183808	+	0.318365i
$671$	−6.72934	−	11.6556i	−0.259783	−	0.449958i
$672$	3.88553	−	6.72993i	0.149888	−	0.259613i
$673$	−34.2732			−1.32113			−0.660567	−	0.750767i	$-0.729684\pi$
$673$	−34.2732			−1.32113			−0.660567	+	0.750767i	$0.729684\pi$
$674$	39.4623			1.52003
$675$	−5.41761	−	9.38358i	−0.208524	−	0.361174i
$676$	8.53031	−	14.7749i	0.328089	−	0.568267i
$677$	14.0954			0.541732			0.270866	−	0.962617i	$-0.412690\pi$
$677$	14.0954			0.541732			0.270866	+	0.962617i	$0.412690\pi$
$678$	2.34837	+	4.06749i	0.0901884	+	0.156211i
$679$	−10.6946	−	18.5236i	−0.410421	−	0.710870i
$680$	−11.3438	−	19.6481i	−0.435016	−	0.753470i
$681$	7.83625	+	13.5728i	0.300286	+	0.520110i
$682$	−28.4734			−1.09030
$683$	11.7903	+	20.4215i	0.451145	+	0.781406i	0.998457	−	0.0555225i	$-0.0176825\pi$
$683$	11.7903	+	20.4215i	0.451145	+	0.781406i	−0.547313	+	0.836928i	$0.684349\pi$
$684$	0.0717868			0.00274484
$685$	18.6404	+	32.2862i	0.712214	+	1.23359i
$686$	21.7798			0.831557
$687$	19.6111			0.748212
$688$	2.84705	+	4.93123i	0.108543	+	0.188001i
$689$	−28.1701	+	48.7921i	−1.07320	+	1.85883i
$690$	−1.16352	−	2.01528i	−0.0442946	−	0.0767206i
$691$	−20.6144	−	35.7051i	−0.784207	−	1.35829i	−0.929471	−	0.368894i	$-0.879737\pi$
$691$	−20.6144	−	35.7051i	−0.784207	−	1.35829i	0.145264	−	0.989393i	$-0.453597\pi$
$692$	−1.47761			−0.0561701
$693$	6.02224			0.228766
$694$	14.5485	+	25.1988i	0.552255	+	0.956533i
$695$	−53.3770			−2.02471
$696$	14.1234	−	24.4625i	0.535346	−	0.927247i
$697$	−11.0021	+	19.0562i	−0.416734	+	0.721805i
$698$	1.63920	−	2.83917i	0.0620446	−	0.107464i
$699$	2.71787	+	4.70749i	0.102799	+	0.178054i
$700$	7.65445	+	13.2579i	0.289311	+	0.501101i
$701$	−7.94337	+	13.7583i	−0.300017	+	0.519644i	−0.976139	−	0.217145i	$-0.930326\pi$
$701$	−7.94337	+	13.7583i	−0.300017	+	0.519644i	0.676123	+	0.736789i	$0.263659\pi$
$702$	−4.12577	−	7.14604i	−0.155717	−	0.269710i
$703$	0.589969			0.0222511
$704$	−9.77930	+	16.9383i	−0.368571	+	0.638384i
$705$	−1.32766	+	2.29957i	−0.0500024	+	0.0866067i
$706$	−2.82451			−0.106302
$707$	−25.7726			−0.969278
$708$	−1.11548	+	1.93207i	−0.0419224	+	0.0726118i
$709$	7.65398	−	13.2571i	0.287451	−	0.497880i	−0.685749	−	0.727838i	$-0.740525\pi$
$709$	7.65398	−	13.2571i	0.287451	−	0.497880i	0.973201	+	0.229958i	$0.0738587\pi$
$710$	29.9430			1.12374
$711$	−2.36235	−	4.09172i	−0.0885952	−	0.153451i
$712$	20.5150	−	35.5330i	0.768832	−	1.33166i
$713$	2.54458	+	4.40735i	0.0952953	+	0.165056i
$714$	3.08851	+	5.34946i	0.115585	+	0.200198i
$715$	29.7711	−	51.5651i	1.11338	−	1.92843i
$716$	−2.46462	+	4.26884i	−0.0921070	+	0.159534i
$717$	−13.9409	+	24.1463i	−0.520631	+	0.901759i
$718$	39.7640			1.48398
$719$	−6.25449	−	10.8331i	−0.233253	−	0.404006i	0.725511	−	0.688211i	$-0.241604\pi$
$719$	−6.25449	−	10.8331i	−0.233253	−	0.404006i	−0.958764	+	0.284205i	$0.908270\pi$
$720$	−10.7280			−0.399809
$721$	46.5065			1.73199
$722$	−11.5537	−	20.0116i	−0.429983	−	0.744753i
$723$	−13.1960	−	22.8562i	−0.490765	−	0.850030i
$724$	2.68249	−	4.64620i	0.0996938	−	0.172675i
$725$	49.9229	+	86.4690i	1.85409	+	3.21138i
$726$	7.45861			0.276815
$727$	12.4642			0.462270			0.231135	−	0.972922i	$-0.425756\pi$
$727$	12.4642			0.462270			0.231135	+	0.972922i	$0.425756\pi$
$728$	28.3394	+	49.0852i	1.05033	+	1.81922i
$729$	1.00000			0.0370370
$730$	−2.97386	−	5.15087i	−0.110067	−	0.190642i
$731$	3.92841			0.145298
$732$	1.57878	+	2.73452i	0.0583532	+	0.101071i
$733$	7.33130	+	12.6982i	0.270788	+	0.469018i	0.969064	−	0.246811i	$-0.0793825\pi$
$733$	7.33130	+	12.6982i	0.270788	+	0.469018i	−0.698276	+	0.715829i	$0.746049\pi$
$734$	−6.61234	−	11.4529i	−0.244066	−	0.422735i
$735$	−0.879341	−	1.52306i	−0.0324350	−	0.0561790i
$736$	1.36834			0.0504377
$737$	2.16805	−	3.75517i	0.0798611	−	0.138323i
$738$	7.20132	+	12.4730i	0.265084	+	0.459139i
$739$	−15.1987			−0.559092			−0.279546	−	0.960132i	$-0.590184\pi$
$739$	−15.1987			−0.559092			−0.279546	+	0.960132i	$0.590184\pi$
$740$	8.77245			0.322482
$741$	−0.469733	+	0.813601i	−0.0172561	+	0.0298884i
$742$	−13.8029	−	23.9073i	−0.506719	−	0.877663i
$743$	10.8734	−	18.8333i	0.398907	−	0.690927i	−0.594685	−	0.803959i	$-0.702723\pi$
$743$	10.8734	−	18.8333i	0.398907	−	0.690927i	0.993591	+	0.113033i	$0.0360564\pi$
$744$	32.4763			1.19064
$745$	−3.98941	+	6.90986i	−0.146161	+	0.253158i
$746$	−34.1861			−1.25164
$747$	−4.51645	+	7.82271i	−0.165248	+	0.286218i
$748$	1.06328	+	1.84165i	0.0388773	+	0.0673374i
$749$	−9.16527	−	15.8747i	−0.334892	−	0.580049i
$750$	14.1344	−	24.4814i	0.516114	−	0.893935i
$751$	−3.76212	+	6.51618i	−0.137282	+	0.237779i	−0.926467	−	0.376377i	$-0.877170\pi$
$751$	−3.76212	+	6.51618i	−0.137282	+	0.237779i	0.789185	+	0.614155i	$0.210503\pi$
$752$	0.899457	+	1.55791i	0.0327998	+	0.0568110i
$753$	−5.66654			−0.206500
$754$	38.0186	+	65.8502i	1.38456	+	2.39812i
$755$	7.03356	+	12.1825i	0.255978	+	0.443366i
$756$	−1.41288			−0.0513860
$757$	−16.2040			−0.588944			−0.294472	−	0.955660i	$-0.595144\pi$
$757$	−16.2040			−0.588944			−0.294472	+	0.955660i	$0.595144\pi$
$758$	−30.0832			−1.09267
$759$	0.530203	+	0.918339i	0.0192452	+	0.0333336i
$760$	0.845361	+	1.46421i	0.0306645	+	0.0531124i
$761$	16.4508	−	28.4936i	0.596340	−	1.03289i	−0.397016	−	0.917812i	$-0.629954\pi$
$761$	16.4508	−	28.4936i	0.596340	−	1.03289i	0.993356	−	0.115080i	$-0.0367123\pi$
$762$	4.48378			0.162430
$763$	−21.9197	+	37.9660i	−0.793545	+	1.37446i
$764$	3.93864	−	6.82193i	0.142495	−	0.246809i
$765$	−3.70068	+	6.40977i	−0.133799	+	0.231746i
$766$	11.3026	−	19.5767i	0.408380	−	0.707335i
$767$	−14.5982	−	25.2848i	−0.527111	−	0.912983i
$768$	5.76228	−	9.98056i	0.207928	−	0.360142i
$769$	39.9868			1.44196			0.720980	−	0.692955i	$-0.243692\pi$
$769$	39.9868			1.44196			0.720980	+	0.692955i	$0.243692\pi$
$770$	14.5873	+	25.2660i	0.525691	+	0.910524i
$771$	0.789607			0.0284370
$772$	−0.843744	−	1.46141i	−0.0303670	−	0.0525972i
$773$	−6.04371	+	10.4680i	−0.217377	+	0.376508i	−0.954005	−	0.299790i	$-0.903083\pi$
$773$	−6.04371	+	10.4680i	−0.217377	+	0.376508i	0.736628	+	0.676298i	$0.236417\pi$
$774$	1.28565	−	2.22681i	0.0462118	−	0.0800412i
$775$	−57.3980	+	99.4163i	−2.06180	+	3.57114i
$776$	−12.0171	−	20.8142i	−0.431388	−	0.747186i
$777$	−11.6115			−0.416562
$778$	−39.2495			−1.40716
$779$	0.819895	−	1.42010i	0.0293758	−	0.0508804i
$780$	−6.98463	+	12.0977i	−0.250090	+	0.433168i
$781$	−13.6446			−0.488243
$782$	−0.543830	+	0.941941i	−0.0194473	+	0.0336838i
$783$	−9.21492			−0.329314
$784$	−1.19147			−0.0425524
$785$	47.6435	−	14.7047i	1.70047	−	0.524834i
$786$	−9.10888			−0.324903
$787$	−2.94048			−0.104817			−0.0524083	−	0.998626i	$-0.516690\pi$
$787$	−2.94048			−0.104817			−0.0524083	+	0.998626i	$0.516690\pi$
$788$	−2.40324	+	4.16254i	−0.0856119	+	0.148284i
$789$	−25.7500			−0.916723
$790$	11.4444	−	19.8223i	0.407174	−	0.705245i
$791$	−5.26227	+	9.11452i	−0.187105	+	0.324075i
$792$	6.76694			0.240453
$793$	−41.3225			−1.46741
$794$	−3.00658	−	5.20755i	−0.106700	−	0.184809i
$795$	16.5387	−	28.6459i	0.586568	−	1.01597i
$796$	1.29210	−	2.23798i	0.0457971	−	0.0793230i
$797$	1.68152	−	2.91248i	0.0595626	−	0.103165i	−0.834707	−	0.550695i	$-0.814363\pi$
$797$	1.68152	−	2.91248i	0.0595626	−	0.103165i	0.894269	+	0.447530i	$0.147696\pi$
$798$	−0.230161	−	0.398650i	−0.00814761	−	0.0141121i
$799$	1.24109			0.0439066
$800$	15.4328	+	26.7304i	0.545632	+	0.945062i
$801$	−13.3852			−0.472942
$802$	8.41776	−	14.5800i	0.297241	−	0.514837i
$803$	1.35515	+	2.34718i	0.0478221	+	0.0828303i
$804$	−0.508647	+	0.881002i	−0.0179386	+	0.0310706i
$805$	2.60725	−	4.51589i	0.0918936	−	0.159164i
$806$	−43.7113	+	75.7102i	−1.53966	+	2.66678i
$807$	1.89949	−	3.29002i	0.0668653	−	0.115814i
$808$	−28.9596			−1.01880
$809$	−12.9790	+	22.4803i	−0.456317	+	0.790365i	−0.998763	−	0.0497262i	$-0.984165\pi$
$809$	−12.9790	+	22.4803i	−0.456317	+	0.790365i	0.542446	+	0.840091i	$0.317498\pi$
$810$	2.42225	+	4.19545i	0.0851090	+	0.147413i
$811$	−28.2432	−	48.9187i	−0.991754	−	1.71777i	−0.606861	−	0.794808i	$-0.707571\pi$
$811$	−28.2432	−	48.9187i	−0.991754	−	1.71777i	−0.384894	−	0.922961i	$-0.625762\pi$
$812$	13.0196			0.456898
$813$	−7.87966			−0.276352
$814$	11.4392			0.400945
$815$	−32.1651	−	55.7115i	−1.12669	−	1.95149i
$816$	2.50713	+	4.34248i	0.0877671	+	0.152017i
$817$	−0.292752			−0.0102421
$818$	3.82686	+	6.62832i	0.133803	+	0.231754i
$819$	9.24511	−	16.0130i	0.323050	−	0.559540i
$820$	12.1913	−	21.1160i	0.425739	−	0.737402i
$821$	5.44860	+	9.43725i	0.190157	+	0.329362i	0.945302	−	0.326196i	$-0.105767\pi$
$821$	5.44860	+	9.43725i	0.190157	+	0.329362i	−0.755145	+	0.655558i	$0.772433\pi$
$822$	−5.70269	−	9.87735i	−0.198904	−	0.344512i
$823$	17.0020	−	29.4483i	0.592651	−	1.02650i	−0.401222	−	0.915981i	$-0.631415\pi$
$823$	17.0020	−	29.4483i	0.592651	−	1.02650i	0.993874	−	0.110521i	$-0.0352521\pi$
$824$	52.2575			1.82048
$825$	−11.9598	+	20.7149i	−0.416386	+	0.721201i
$826$	14.3057			0.497760
$827$	−13.9280	+	24.1240i	−0.484323	+	0.838872i	−0.999838	−	0.0180086i	$-0.994267\pi$
$827$	−13.9280	+	24.1240i	−0.484323	+	0.838872i	0.515515	+	0.856881i	$0.327601\pi$
$828$	−0.124391	−	0.215452i	−0.00432290	−	0.00748747i
$829$	17.3149	−	29.9903i	0.601372	−	1.04161i	−0.391242	−	0.920288i	$-0.627954\pi$
$829$	17.3149	−	29.9903i	0.601372	−	1.04161i	0.992614	−	0.121319i	$-0.0387123\pi$
$830$	−43.7598			−1.51892
$831$	17.1586			0.595224
$832$	30.0256	+	52.0059i	1.04095	+	1.80298i
$833$	−0.411003	+	0.711878i	−0.0142404	+	0.0246651i
$834$	16.3297			0.565451
$835$	−43.7895	−	75.8456i	−1.51540	−	2.62474i
$836$	−0.0792372	−	0.137243i	−0.00274048	−	0.00474664i
$837$	−5.29735	−	9.17528i	−0.183103	−	0.317144i
$838$	−2.42270	−	4.19625i	−0.0836909	−	0.144957i
$839$	11.2690			0.389050			0.194525	−	0.980898i	$-0.437683\pi$
$839$	11.2690			0.389050			0.194525	+	0.980898i	$0.437683\pi$
$840$	−16.6381	−	28.8180i	−0.574068	−	0.994316i
$841$	55.9148			1.92810
$842$	−2.26383	−	3.92106i	−0.0780166	−	0.135129i
$843$	−12.6554			−0.435876
$844$	−11.4314			−0.393486
$845$	−65.5413	−	113.521i	−2.25469	−	3.90523i
$846$	0.406171	−	0.703510i	0.0139645	−	0.0241872i
$847$	8.35671	+	14.4742i	0.287140	+	0.497341i
$848$	−11.2046	−	19.4070i	−0.384768	−	0.666438i
$849$	−14.9830			−0.514217
$850$	−24.5343			−0.841520
$851$	−1.02229	−	1.77066i	−0.0350437	−	0.0606974i
$852$	3.20117			0.109670
$853$	9.48733	−	16.4325i	0.324840	−	0.562639i	−0.656640	−	0.754204i	$-0.728023\pi$
$853$	9.48733	−	16.4325i	0.324840	−	0.562639i	0.981480	+	0.191565i	$0.0613562\pi$
$854$	10.1237	−	17.5347i	0.346424	−	0.600025i
$855$	0.275781	−	0.477667i	0.00943151	−	0.0163359i
$856$	−10.2986	−	17.8377i	−0.352000	−	0.609682i
$857$	−4.75335	−	8.23304i	−0.162371	−	0.281235i	0.773347	−	0.633983i	$-0.218581\pi$
$857$	−4.75335	−	8.23304i	−0.162371	−	0.281235i	−0.935719	+	0.352747i	$0.885248\pi$
$858$	−9.10792	+	15.7754i	−0.310939	+	0.538563i
$859$	−8.24128	−	14.2743i	−0.281189	−	0.487033i	0.690489	−	0.723343i	$-0.257395\pi$
$859$	−8.24128	−	14.2743i	−0.281189	−	0.487033i	−0.971678	+	0.236310i	$0.924062\pi$
$860$	−4.35303			−0.148437
$861$	−16.1369	+	27.9499i	−0.549943	+	0.952530i
$862$	−0.667550	+	1.15623i	−0.0227368	+	0.0393814i
$863$	16.8656			0.574111			0.287055	−	0.957914i	$-0.407324\pi$
$863$	16.8656			0.574111			0.287055	+	0.957914i	$0.407324\pi$
$864$	−2.84863			−0.0969125
$865$	−5.67647	+	9.83194i	−0.193006	+	0.334296i
$866$	−5.16933	+	8.95355i	−0.175661	+	0.304254i
$867$	−13.5406			−0.459863
$868$	7.48453	+	12.9636i	0.254042	+	0.440013i
$869$	−5.21506	+	9.03276i	−0.176909	+	0.306415i
$870$	−22.3208	−	38.6608i	−0.756746	−	1.31072i
$871$	−6.65661	−	11.5296i	−0.225551	−	0.390665i
$872$	−24.6302	+	42.6608i	−0.834084	+	1.44468i
$873$	−3.92032	+	6.79019i	−0.132683	+	0.229813i
$874$	0.0405271	−	0.0701950i	0.00137085	−	0.00237438i
$875$	63.3452			2.14146
$876$	−0.317932	−	0.550674i	−0.0107419	−	0.0186056i
$877$	27.9365			0.943349			0.471675	−	0.881773i	$-0.343650\pi$
$877$	27.9365			0.943349			0.471675	+	0.881773i	$0.343650\pi$
$878$	−18.2218			−0.614956
$879$	−15.9600	−	27.6436i	−0.538319	−	0.932396i
$880$	11.8414	+	20.5099i	0.399174	+	0.691390i
$881$	8.25814	−	14.3035i	0.278224	−	0.481898i	−0.692720	−	0.721207i	$-0.743588\pi$
$881$	8.25814	−	14.3035i	0.278224	−	0.481898i	0.970943	+	0.239309i	$0.0769210\pi$
$882$	0.269018	+	0.465953i	0.00905830	+	0.0156894i
$883$	−21.3894			−0.719812			−0.359906	−	0.932989i	$-0.617191\pi$
$883$	−21.3894			−0.719812			−0.359906	+	0.932989i	$0.617191\pi$
$884$	6.52921			0.219601
$885$	8.57064	+	14.8448i	0.288099	+	0.499002i
$886$	1.92784			0.0647669
$887$	19.8476	+	34.3770i	0.666417	+	1.15427i	0.978899	+	0.204344i	$0.0655062\pi$
$887$	19.8476	+	34.3770i	0.666417	+	1.15427i	−0.312482	+	0.949924i	$0.601160\pi$
$888$	−13.0474			−0.437843
$889$	5.02368	+	8.70127i	0.168489	+	0.291831i
$890$	−32.4222	−	56.1568i	−1.08679	−	1.88238i
$891$	−1.10379	−	1.91181i	−0.0369782	−	0.0640481i
$892$	−3.04307	−	5.27075i	−0.101889	−	0.176478i
$893$	−0.0924881			−0.00309499
$894$	1.22048	−	2.11394i	0.0408191	−	0.0707007i
$895$	18.9365	+	32.7989i	0.632976	+	1.09635i
$896$	−13.8820			−0.463763
$897$	3.25579			0.108708
$898$	4.12453	−	7.14390i	0.137638	−	0.238395i
$899$	48.8147	+	84.5495i	1.62806	+	2.81988i
$900$	2.80589	−	4.85994i	0.0935296	−	0.161998i
$901$	−15.4604			−0.515059
$902$	15.8974	−	27.5351i	0.529326	−	0.916820i
$903$	5.76183			0.191742
$904$	−5.91300	+	10.2416i	−0.196663	+	0.340631i
$905$	−20.6104	−	35.6983i	−0.685114	−	1.18665i
$906$	−2.15179	−	3.72700i	−0.0714883	−	0.123821i
$907$	−19.5241	+	33.8167i	−0.648287	+	1.12287i	0.335244	+	0.942131i	$0.391181\pi$
$907$	−19.5241	+	33.8167i	−0.648287	+	1.12287i	−0.983532	+	0.180735i	$0.942152\pi$
$908$	−4.05855	+	7.02961i	−0.134688	+	0.233286i
$909$	4.72373	+	8.18174i	0.156676	+	0.271371i
$910$	89.5757			2.96941
$911$	4.21647	+	7.30313i	0.139698	+	0.241964i	0.927382	−	0.374115i	$-0.122054\pi$
$911$	4.21647	+	7.30313i	0.139698	+	0.241964i	−0.787684	+	0.616079i	$0.788720\pi$
$912$	−0.186835	−	0.323608i	−0.00618674	−	0.0107157i
$913$	19.9408			0.659943
$914$	27.2383			0.900961
$915$	24.2605			0.802028
$916$	5.07850	+	8.79621i	0.167798	+	0.290635i
$917$	−10.2057	−	17.6768i	−0.337022	−	0.583739i
$918$	1.13215	−	1.96095i	0.0373667	−	0.0647210i
$919$	30.6636			1.01150			0.505750	−	0.862680i	$-0.331216\pi$
$919$	30.6636			1.01150			0.505750	+	0.862680i	$0.331216\pi$
$920$	2.92966	−	5.07432i	0.0965881	−	0.167295i
$921$	−9.67814	+	16.7630i	−0.318905	+	0.552360i
$922$	−10.1611	+	17.5996i	−0.334639	+	0.579611i
$923$	−20.9467	+	36.2807i	−0.689469	+	1.19420i
$924$	1.55952	+	2.70116i	0.0513044	+	0.0888618i
$925$	23.0598	−	39.9407i	0.758200	−	1.31324i
$926$	−44.9845			−1.47828
$927$	−8.52394	−	14.7639i	−0.279963	−	0.484910i
$928$	26.2499			0.861697
$929$	18.4053	+	31.8789i	0.603858	+	1.04591i	0.992231	+	0.124411i	$0.0397041\pi$
$929$	18.4053	+	31.8789i	0.603858	+	1.04591i	−0.388372	+	0.921502i	$0.626963\pi$
$930$	25.6630	−	44.4496i	0.841522	−	1.45756i
$931$	0.0306286	−	0.0530503i	0.00100381	−	0.00173865i
$932$	−1.40764	+	2.43810i	−0.0461087	+	0.0798627i
$933$	12.1814	+	21.0989i	0.398803	+	0.690746i
$934$	−24.9850			−0.817534
$935$	16.3390			0.534344
$936$	10.3883	−	17.9931i	0.339554	−	0.588124i
$937$	−7.44214	+	12.8902i	−0.243124	+	0.421103i	−0.961603	−	0.274446i	$-0.911506\pi$
$937$	−7.44214	+	12.8902i	−0.243124	+	0.421103i	0.718478	+	0.695549i	$0.244839\pi$
$938$	6.52324			0.212991
$939$	−0.980188	+	1.69774i	−0.0319872	+	0.0554035i
$940$	−1.37524			−0.0448553
$941$	4.08844			0.133279			0.0666397	−	0.997777i	$-0.478772\pi$
$941$	4.08844			0.133279			0.0666397	+	0.997777i	$0.478772\pi$
$942$	−14.5756	+	4.49864i	−0.474900	+	0.146573i
$943$	−5.68282			−0.185058
$944$	11.6128			0.377965
$945$	−5.42782	+	9.40126i	−0.176567	+	0.305823i
$946$	−5.67633			−0.184553
$947$	−17.9747	+	31.1330i	−0.584098	+	1.01169i	0.410889	+	0.911685i	$0.365218\pi$
$947$	−17.9747	+	31.1330i	−0.584098	+	1.01169i	−0.994987	+	0.100002i	$0.968115\pi$
$948$	1.22351	−	2.11918i	0.0397377	−	0.0688278i
$949$	8.32148			0.270127
$950$	1.82834			0.0593191
$951$	−0.975394	−	1.68943i	−0.0316293	−	0.0547836i
$952$	−7.77662	+	13.4695i	−0.252042	+	0.436549i
$953$	−0.769308	+	1.33248i	−0.0249203	+	0.0431633i	−0.878217	−	0.478263i	$-0.841267\pi$
$953$	−0.769308	+	1.33248i	−0.0249203	+	0.0431633i	0.853296	+	0.521426i	$0.174600\pi$
$954$	−5.05971	+	8.76367i	−0.163814	+	0.283734i
$955$	−30.2619	−	52.4152i	−0.979253	−	1.69612i
$956$	−14.4405			−0.467039
$957$	10.1713	+	17.6172i	0.328791	+	0.569483i
$958$	9.42651			0.304557
$959$	12.7787	−	22.1334i	0.412646	−	0.714724i
$960$	−17.6281	−	30.5328i	−0.568945	−	0.985441i
$961$	−40.6239	+	70.3626i	−1.31045	+	2.26976i
$962$	17.5611	−	30.4167i	0.566192	−	0.980673i
$963$	−3.35971	+	5.81919i	−0.108265	+	0.187521i
$964$	6.83447	−	11.8376i	0.220123	−	0.381265i
$965$	−12.9655			−0.417375
$966$	−0.797640	+	1.38155i	−0.0256636	+	0.0444507i
$967$	−25.7035	−	44.5198i	−0.826570	−	1.43166i	−0.900713	−	0.434414i	$-0.856956\pi$
$967$	−25.7035	−	44.5198i	−0.826570	−	1.43166i	0.0741432	−	0.997248i	$-0.476378\pi$
$968$	9.39008	+	16.2641i	0.301809	+	0.522748i
$969$	−0.257799			−0.00828171
$970$	−37.9839			−1.21959
$971$	44.1096			1.41554			0.707772	−	0.706441i	$-0.249700\pi$
$971$	44.1096			1.41554			0.707772	+	0.706441i	$0.249700\pi$
$972$	0.258960	+	0.448531i	0.00830614	+	0.0143867i
$973$	18.2960	+	31.6896i	0.586542	+	1.01592i
$974$	16.5918			0.531637
$975$	36.7204	+	63.6015i	1.17599	+	2.03688i
$976$	8.21798	−	14.2340i	0.263051	−	0.455618i
$977$	−1.46014	+	2.52904i	−0.0467141	+	0.0809111i	−0.888437	−	0.458999i	$-0.848208\pi$
$977$	−1.46014	+	2.52904i	−0.0467141	+	0.0809111i	0.841723	+	0.539910i	$0.181542\pi$
$978$	9.84030	+	17.0439i	0.314658	+	0.545004i
$979$	14.7744	+	25.5899i	0.472190	+	0.817858i
$980$	0.455428	−	0.788824i	0.0145481	−	0.0251981i
$981$	16.0702			0.513081
$982$	18.4042	−	31.8771i	0.587303	−	1.01724i
$983$	32.6621			1.04176			0.520880	−	0.853630i	$-0.325604\pi$
$983$	32.6621			1.04176			0.520880	+	0.853630i	$0.325604\pi$
$984$	−18.1323	+	31.4061i	−0.578038	+	1.00119i
$985$	18.4649	+	31.9822i	0.588341	+	1.01904i
$986$	−10.4327	+	18.0700i	−0.332245	+	0.575466i
$987$	1.82032			0.0579413
$988$	−0.486568			−0.0154798
$989$	0.507277	+	0.878629i	0.0161305	+	0.0279388i
$990$	5.34728	−	9.26176i	0.169948	−	0.294358i
$991$	−29.3375			−0.931937			−0.465968	−	0.884801i	$-0.654294\pi$
$991$	−29.3375			−0.931937			−0.465968	+	0.884801i	$0.654294\pi$
$992$	15.0902	+	26.1370i	0.479115	+	0.829851i
$993$	1.19158	+	2.06387i	0.0378135	+	0.0654950i
$994$	−10.2635	−	17.7769i	−0.325539	−	0.563850i
$995$	−9.92761	−	17.1951i	−0.314726	−	0.545122i
$996$	−4.67831			−0.148238
$997$	20.9204	+	36.2352i	0.662557	+	1.14758i	0.979942	+	0.199285i	$0.0638619\pi$
$997$	20.9204	+	36.2352i	0.662557	+	1.14758i	−0.317385	+	0.948297i	$0.602805\pi$
$998$	14.4542			0.457540
$999$	2.12822	+	3.68619i	0.0673339	+	0.116626i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.e.c.301.4	yes	28
157.12	even	3	inner	471.2.e.c.169.4	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.e.c.169.4	✓	28	157.12	even	3	inner
471.2.e.c.301.4	yes	28	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.21741 q^{2} +(-0.500000 + 0.866025i) q^{3} -0.517920 q^{4} +(-1.98968 + 3.44622i) q^{5} +(0.608704 - 1.05431i) q^{6} +2.72799 q^{7} +3.06533 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-1.21741 q^{2} +(-0.500000 + 0.866025i) q^{3} -0.517920 q^{4} +(-1.98968 + 3.44622i) q^{5} +(0.608704 - 1.05431i) q^{6} +2.72799 q^{7} +3.06533 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.42225 - 4.19545i) q^{10} +(-1.10379 + 1.91181i) q^{11} +(0.258960 - 0.448531i) q^{12} +(3.38898 + 5.86988i) q^{13} -3.32108 q^{14} +(-1.98968 - 3.44622i) q^{15} -2.69592 q^{16} +(-0.929972 + 1.61076i) q^{17} +(0.608704 + 1.05431i) q^{18} +(0.0693030 - 0.120036i) q^{19} +(1.03049 - 1.78486i) q^{20} +(-1.36400 + 2.36251i) q^{21} +(1.34376 - 2.32745i) q^{22} -0.480350 q^{23} +(-1.53267 + 2.65466i) q^{24} +(-5.41761 - 9.38358i) q^{25} +(-4.12577 - 7.14604i) q^{26} +1.00000 q^{27} -1.41288 q^{28} -9.21492 q^{29} +(2.42225 + 4.19545i) q^{30} +(-5.29735 - 9.17528i) q^{31} -2.84863 q^{32} +(-1.10379 - 1.91181i) q^{33} +(1.13215 - 1.96095i) q^{34} +(-5.42782 + 9.40126i) q^{35} +(0.258960 + 0.448531i) q^{36} +(2.12822 + 3.68619i) q^{37} +(-0.0843700 + 0.146133i) q^{38} -6.77796 q^{39} +(-6.09902 + 10.5638i) q^{40} +11.8306 q^{41} +(1.66054 - 2.87614i) q^{42} +(-1.05606 - 1.82914i) q^{43} +(0.571672 - 0.990165i) q^{44} +3.97935 q^{45} +0.584781 q^{46} +(-0.333636 - 0.577875i) q^{47} +(1.34796 - 2.33474i) q^{48} +0.441952 q^{49} +(6.59544 + 11.4236i) q^{50} +(-0.929972 - 1.61076i) q^{51} +(-1.75522 - 3.04013i) q^{52} +(4.15614 + 7.19864i) q^{53} -1.21741 q^{54} +(-4.39235 - 7.60777i) q^{55} +8.36221 q^{56} +(0.0693030 + 0.120036i) q^{57} +11.2183 q^{58} -4.30756 q^{59} +(1.03049 + 1.78486i) q^{60} +(-3.04830 + 5.27981i) q^{61} +(6.44904 + 11.1701i) q^{62} +(-1.36400 - 2.36251i) q^{63} +8.85979 q^{64} -26.9719 q^{65} +(1.34376 + 2.32745i) q^{66} -1.96419 q^{67} +(0.481651 - 0.834243i) q^{68} +(0.240175 - 0.415995i) q^{69} +(6.60787 - 11.4452i) q^{70} +(3.09041 + 5.35276i) q^{71} +(-1.53267 - 2.65466i) q^{72} +(0.613864 - 1.06324i) q^{73} +(-2.59091 - 4.48759i) q^{74} +10.8352 q^{75} +(-0.0358934 + 0.0621692i) q^{76} +(-3.01112 + 5.21541i) q^{77} +8.25153 q^{78} +4.72471 q^{79} +(5.36401 - 9.29073i) q^{80} +(-0.500000 + 0.866025i) q^{81} -14.4026 q^{82} +(-4.51645 - 7.82271i) q^{83} +(0.706441 - 1.22359i) q^{84} +(-3.70068 - 6.40977i) q^{85} +(1.28565 + 2.22681i) q^{86} +(4.60746 - 7.98036i) q^{87} +(-3.38347 + 5.86034i) q^{88} +(6.69258 - 11.5919i) q^{89} -4.84449 q^{90} +(9.24511 + 16.0130i) q^{91} +0.248783 q^{92} +10.5947 q^{93} +(0.406171 + 0.703510i) q^{94} +(0.275781 + 0.477667i) q^{95} +(1.42432 - 2.46699i) q^{96} +(-3.92032 - 6.79019i) q^{97} -0.538036 q^{98} +2.20757 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9}+O(q^{10}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9} - q^{10} + 2 q^{11} - 13 q^{12} - 14 q^{14} - 2 q^{15} + 14 q^{16} + 3 q^{17} - q^{18} - 11 q^{19} + q^{20} - 2 q^{21} - 2 q^{22} - 6 q^{23} - 20 q^{25} + 12 q^{26} + 28 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 14 q^{31} + 12 q^{32} + 2 q^{33} - 15 q^{34} - 13 q^{35} - 13 q^{36} - q^{37} + 18 q^{38} - 8 q^{40} + 16 q^{41} + 7 q^{42} - 16 q^{43} + 12 q^{44} + 4 q^{45} + 16 q^{46} - 29 q^{47} - 7 q^{48} + 44 q^{49} - 29 q^{50} + 3 q^{51} + 27 q^{52} + 6 q^{53} + 2 q^{54} - 29 q^{55} - 26 q^{56} - 11 q^{57} + 62 q^{58} - 8 q^{59} + q^{60} + 14 q^{61} + 52 q^{62} - 2 q^{63} + 16 q^{64} - 52 q^{65} - 2 q^{66} + 36 q^{67} + 6 q^{68} + 3 q^{69} - 37 q^{70} - 27 q^{71} - 10 q^{73} - 5 q^{74} + 40 q^{75} - 43 q^{76} + 11 q^{77} - 24 q^{78} - 16 q^{79} - 26 q^{80} - 14 q^{81} - 24 q^{82} + 12 q^{83} - q^{84} + 12 q^{85} - 56 q^{86} + 5 q^{87} + 47 q^{88} - 13 q^{89} + 2 q^{90} + 13 q^{91} - 50 q^{92} + 28 q^{93} - 40 q^{94} - 7 q^{95} - 6 q^{96} + 6 q^{97} - 46 q^{98} - 4 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9 - q^10 + 2 * q^11 - 13 * q^12 - 14 * q^14 - 2 * q^15 + 14 * q^16 + 3 * q^17 - q^18 - 11 * q^19 + q^20 - 2 * q^21 - 2 * q^22 - 6 * q^23 - 20 * q^25 + 12 * q^26 + 28 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 14 * q^31 + 12 * q^32 + 2 * q^33 - 15 * q^34 - 13 * q^35 - 13 * q^36 - q^37 + 18 * q^38 - 8 * q^40 + 16 * q^41 + 7 * q^42 - 16 * q^43 + 12 * q^44 + 4 * q^45 + 16 * q^46 - 29 * q^47 - 7 * q^48 + 44 * q^49 - 29 * q^50 + 3 * q^51 + 27 * q^52 + 6 * q^53 + 2 * q^54 - 29 * q^55 - 26 * q^56 - 11 * q^57 + 62 * q^58 - 8 * q^59 + q^60 + 14 * q^61 + 52 * q^62 - 2 * q^63 + 16 * q^64 - 52 * q^65 - 2 * q^66 + 36 * q^67 + 6 * q^68 + 3 * q^69 - 37 * q^70 - 27 * q^71 - 10 * q^73 - 5 * q^74 + 40 * q^75 - 43 * q^76 + 11 * q^77 - 24 * q^78 - 16 * q^79 - 26 * q^80 - 14 * q^81 - 24 * q^82 + 12 * q^83 - q^84 + 12 * q^85 - 56 * q^86 + 5 * q^87 + 47 * q^88 - 13 * q^89 + 2 * q^90 + 13 * q^91 - 50 * q^92 + 28 * q^93 - 40 * q^94 - 7 * q^95 - 6 * q^96 + 6 * q^97 - 46 * q^98 - 4 * q^99

Introduction

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